Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
199201	Simplify	(x+y)/(2xy-y^2)-(x-y)/(2x^2-xy)	$\frac{x + y}{2 x y - y^{2}} - \frac{x - y}{2 x^{2} - x y}$
199202	Simplify	square root of 2x^4* square root of 8x^3	$\sqrt{2 x^{4}} \cdot \sqrt{8 x^{3}}$
199203	Simplify	cube root of square root of 27	$\sqrt[3]{\sqrt{27}}$
199204	Solve for y	2xy+6y=10	$2 x y + 6 y = 10$
199205	Solve for x	square root of 2x-2/3=0	$\sqrt{2 x} - \frac{2}{3} = 0$
199206	Graph	y> = square root of x-2+1	$y \geq \sqrt{x - 2} + 1$
199207	Solve for n	1+2cot(theta)^2+cot(theta)^4=csc(theta)^n	$1 + 2 \cot^{2} (θ) + \cot^{4} (θ) = {\csc (θ)}^{n}$
199208	Solve for z	2/y=x/(3z)	$\frac{2}{y} = \frac{x}{3 z}$
199209	Solve for y	x-1/3y=-1	$x - \frac{1}{3} y = - 1$
199210	Solve for k	cube root of k+4 = cube root of 2k+3	$\sqrt[3]{k + 4} = \sqrt[3]{2 k + 3}$
199211	Solve the System of Inequalities	y<=-3x+1 y>=-1/4x+6	$y \leq - 3 x + 1$ $y \geq - \frac{1}{4} x + 6$
199212	Simplify	((2x^3)^2(3y^4)^3)/(12x^4y^5)-4x^2y^7	$\frac{{(2 x^{3})}^{2} {(3 y^{4})}^{3}}{12 x^{4} y^{5}} - 4 x^{2} y^{7}$
199213	Simplify	( cube root of 625x^6y^4)/( cube root of 5xy)	$\frac{\sqrt[3]{625 x^{6} y^{4}}}{\sqrt[3]{5 x y}}$
199214	Simplify	(1+i square root of 2)/2-(1-i square root of 1/2)	$\frac{(1 + i \sqrt{2})}{2} - (1 - i \sqrt{\frac{1}{2}})$
199215	Factor	(b-c)^3+(c-a)^3+(a-b)^3	${(b - c)}^{3} + {(c - a)}^{3} + {(a - b)}^{3}$
199216	Find the Product	(3a-b+2c)^2	${(3 a - b + 2 c)}^{2}$
199217	Simplify the Radical Expression	5/(3- square root of 2)	$\frac{5}{3 - \sqrt{2}}$
199218	Simplify	(a^2-b^2)/(a^2-a+ab-b)	$\frac{a^{2} - b^{2}}{a^{2} - a + a b - b}$
199219	Solve for t	7/12t-1/4=5/6	$\frac{7}{12} t - \frac{1}{4} = \frac{5}{6}$
199220	Simplify	(mx+my)/(5n)*(10m)/(ny+nx)	$\frac{m x + m y}{5 n} \cdot \frac{10 m}{n y + n x}$
199221	Solve the Inequality for x	(x+3)/((x-4)^2(x^2-4))<=0	$\frac{x + 3}{{(x - 4)}^{2} (x^{2} - 4)} \leq 0$
199222	Evaluate	(2^-2m^-3)/(n^0)	$\frac{2^{- 2} m^{- 3}}{n^{0}}$
199223	Solve for y	1/3y=2/3y^2	$\frac{1}{3} y = \frac{2}{3} y^{2}$
199224	Simplify	(30c^2+19ac-63a^2)/(6c-7a)	$\frac{30 c^{2} + 19 a c - 63 a^{2}}{6 c - 7 a}$
199225	Solve for x	2x^2(x-1)=0	$2 x^{2} (x - 1) = 0$
199226	Simplify	3(5-12)+4÷2	$3 (5 - 12) + 4 \div 2$
199227	Simplify	-3xy(x^3y^3-3x^2y+7xy^2)	$- 3 x y (x^{3} y^{3} - 3 x^{2} y + 7 x y^{2})$
199228	Evaluate	(s^-5)^3	${(s^{- 5})}^{3}$
199229	Simplify the Radical Expression	square root of cube root of 64	$\sqrt{\sqrt[3]{64}}$
199230	Simplify	17(a^(2n+1))^42a^(7n-12)	$17 \cdot {(a^{2 n + 1})}^{4} \cdot 2 a^{7 n - 12}$
199231	Solve for x	3.4/(2x-12)=18/4.5	$\frac{3.4}{2 x - 12} = \frac{18}{4.5}$
199232	Divide	( cube root of 48x^3y^7)/( cube root of 8x^5y)	$\frac{\sqrt[3]{48 x^{3} y^{7}}}{\sqrt[3]{8 x^{5} y}}$
199233	Simplify	(36x^4y^5)/((3xy)^2)	$\frac{36 x^{4} y^{5}}{{(3 x y)}^{2}}$
199234	Simplify	(16a^4+16a)/(a^2+1-a)	$\frac{16 a^{4} + 16 a}{a^{2} + 1 - a}$
199235	Solve the Rational Equation for x	square root of x=9	$\sqrt{x} = 9$
199236	Simplify	(x^16y^20z^8)^(1/4)	${(x^{16} y^{20} z^{8})}^{\frac{1}{4}}$
199237	Simplify	(x^2-1)/(5xy)*(x^2y)/(1+x)	$\frac{x^{2} - 1}{5 x y} \cdot \frac{x^{2} y}{1 + x}$
199238	Simplify	((3m^2n^3)/(xy^2))^2((x^3yz^2)/(2mn^2))^3	${(\frac{3 m^{2} n^{3}}{x y^{2}})}^{2} {(\frac{x^{3} y z^{2}}{2 m n^{2}})}^{3}$
199239	Simplify	15 root of x^10b^15	$\sqrt[15]{x^{10} b^{15}}$
199240	Simplify	(25a^5b^3c)/(5ab^4c)	$\frac{25 a^{5} b^{3} c}{5 a b^{4} c}$
199241	Simplify	(5 square root of 3+ square root of 15)*(3 square root of 5- square root of 15)	$(5 \sqrt{3} + \sqrt{15}) \cdot (3 \sqrt{5} - \sqrt{15})$
199242	Solve for θ	-2cos(theta)^2+sin(theta)+1=0	$- 2 \cos^{2} (θ) + \sin (θ) + 1 = 0$
199243	Simplify	13(8^(3/4))-4*8^(3/4)	$13 (8^{\frac{3}{4}}) - 4 \cdot 8^{\frac{3}{4}}$
199244	Simplify	( square root of 3- square root of 6+ square root of 12- square root of 24)*( square root of 6)/2	$(\sqrt{3} - \sqrt{6} + \sqrt{12} - \sqrt{24}) \cdot \frac{\sqrt{6}}{2}$
199245	Solve for z	(2z-3)/5-(z-6)/4=3	$\frac{2 z - 3}{5} - \frac{z - 6}{4} = 3$
199246	Factor	2x-4xy+10y-5	$2 x - 4 x y + 10 y - 5$
199247	Simplify	(2b)/(2b+3)+5/(3-2b)-(4b^2+9)/(4b^2-9)	$\frac{2 b}{2 b + 3} + \frac{5}{3 - 2 b} - \frac{4 b^{2} + 9}{4 b^{2} - 9}$
199248	Simplify the Radical Expression	( square root of 2+ square root of 5)/( square root of 2- square root of 5)	$\frac{\sqrt{2} + \sqrt{5}}{\sqrt{2} - \sqrt{5}}$
199249	Solve for x	(3x-4b)+(7b+2x)=13b	$(3 x - 4 b) + (7 b + 2 x) = 13 b$
199250	Solve for x	4x(5x+7)=4(5x^2+8x+4)	$4 x (5 x + 7) = 4 (5 x^{2} + 8 x + 4)$
199251	Simplify	(a-2y)/(a+y)-(y^2-5ay)/(a^2-y^2)	$\frac{a - 2 y}{a + y} - \frac{y^{2} - 5 a y}{a^{2} - y^{2}}$
199252	Simplify	(5^(1/2)*5^(-3/2))^(-1/4)	${(5^{\frac{1}{2}} \cdot 5^{- \frac{3}{2}})}^{- \frac{1}{4}}$
199253	Evaluate	(5/8-1/3)÷(2/5+1)	$(\frac{5}{8} - \frac{1}{3}) \div (\frac{2}{5} + 1)$
199254	Simplify	8-5y+2x-3+4y+2+4x-2	$8 - 5 y + 2 x - 3 + 4 y + 2 + 4 x - 2$
199255	Simplify	5(x^(2n-1))*(2x^(3n+1))^2	$5 (x^{2 n - 1}) \cdot {(2 x^{3 n + 1})}^{2}$
199256	Rationalize the Denominator	(4- square root of 5)/( square root of 5)	$\frac{4 - \sqrt{5}}{\sqrt{5}}$
199257	Solve for x	2/y=x/(3z)	$\frac{2}{y} = \frac{x}{3 z}$
199258	Solve for x	x^2+x(6-2x)=(x-1)(2-x)-2	$x^{2} + x (6 - 2 x) = (x - 1) (2 - x) - 2$
199259	Simplify	(1/(csc(x)))(tan(x)+cot(x))	$(\frac{1}{\csc (x)}) (\tan (x) + \cot (x))$
199260	Simplify	(4y)/(3x^2+2xy)-(9x)/(3xy+2y^2)	$\frac{4 y}{3 x^{2} + 2 x y} - \frac{9 x}{3 x y + 2 y^{2}}$
199261	Evaluate	(32^20-52^19)/((-2^6)^3)	$\frac{3 \cdot 2^{20} - 5 \cdot 2^{19}}{{(- 2^{6})}^{3}}$
199262	Solve for x	x-1/9=1/6	$x - \frac{1}{9} = \frac{1}{6}$
199263	Graph	y>=3-x y<5x-2	$y \geq 3 - x$ $y < 5 x - 2$
199264	Divide	(28p^3q^2r-36p^2r^2+16q^5r^4)/(4pq^2r)	$\frac{28 p^{3} q^{2} r - 36 p^{2} r^{2} + 16 q^{5} r^{4}}{4 p q^{2} r}$
199265	Simplify	square root of 3^3*6^3	$\sqrt{3^{3} \cdot 6^{3}}$
199266	Solve the System of Inequalities	y>3x-5 y>-x+2	$y > 3 x - 5$ $y > - x + 2$
199267	Evaluate	(p^-8)/(7^-2q^-9)	$\frac{p^{- 8}}{7^{- 2} q^{- 9}}$
199268	Simplify	(a^2-b^2)/(a^2-3a)*(2a-6)/((a+b)^2)	$\frac{a^{2} - b^{2}}{a^{2} - 3 a} \cdot \frac{2 a - 6}{{(a + b)}^{2}}$
199269	Simplify	3x(x^2-4)(5-3x)	$3 x (x^{2} - 4) (5 - 3 x)$
199270	Simplify the Radical Expression	-2x square root of 3xy^3z^7	$- 2 x \sqrt{3 x y^{3} z^{7}}$
199271	Simplify the Radical Expression	( cube root of 5)/( cube root of 4)	$\frac{\sqrt[3]{5}}{\sqrt[3]{4}}$
199272	Solve for y	square root of y^6=-y^3	$\sqrt{y^{6}} = - y^{3}$
199273	Simplify	1/5pq-3/10pq^3-3/5pq^3-7/10pq+3pq	$\frac{1}{5} p q - \frac{3}{10} p q^{3} - \frac{3}{5} p q^{3} - \frac{7}{10} p q + 3 p q$
199274	Graph	y>x-5 y>=-2x	$y > x - 5$ $y \geq - 2 x$
199275	Simplify	1/5m^3-3/4p^2+4/5m^3+3/4p^2	$\frac{1}{5} m^{3} - \frac{3}{4} p^{2} + \frac{4}{5} m^{3} + \frac{3}{4} p^{2}$
199276	Solve for x	3(-2x+1)-2(x+13)=7x-4(1-x)	$3 (- 2 x + 1) - 2 (x + 13) = 7 x - 4 (1 - x)$
199277	Evaluate	0.25^22.4+0.252.4^2-0.252.40.65	${0.25}^{2} \cdot 2.4 + 0.25 \cdot {2.4}^{2} - 0.25 \cdot 2.4 \cdot 0.65$
199278	Simplify	(x^9yz^4)^5	${(x^{9} y z^{4})}^{5}$
199279	Convert to Radical Form	(26)^(1/4)	${(26)}^{\frac{1}{4}}$
199280	Evaluate	(2 4/9-5 2/3)/2 1/3	$\frac{2 \frac{4}{9} - 5 \frac{2}{3}}{2 \frac{1}{3}}$
199281	Graph	f(x)=(X+3)^2-1	$f (x) = {(X + 3)}^{2} - 1$
199282	Simplify	-5x^-5x^0	$- 5 x^{- 5} x^{0}$
199283	Factor	x^3-y^3-x^2y+xy^2	$x^{3} - y^{3} - x^{2} y + x y^{2}$
199284	Simplify	(p^21q^-15r^-3)^(1/3)	${(p^{21} q^{- 15} r^{- 3})}^{\frac{1}{3}}$
199285	Simplify	(4y)/(x-3y)+(2x-2y)/(3y-x)	$\frac{4 y}{x - 3 y} + \frac{2 x - 2 y}{3 y - x}$
199286	Evaluate	9(3^-2)-(3^4)/(3^2)-( square root of 2^6)÷2	$9 (3^{- 2}) - \frac{3^{4}}{3^{2}} - \sqrt{2^{6}} \div 2$
199287	Graph	3x-y^2=8y+1	$3 x - y^{2} = 8 y + 1$
199288	Factor	ab-8a-bx+8x	$a b - 8 a - b x + 8 x$
199289	Solve for x	2(x+11)^(1/2)=x+3	$2 {(x + 11)}^{\frac{1}{2}} = x + 3$
199290	Simplify	a/(2a-b)+(3a-b)/(b-2a)	$\frac{a}{2 a - b} + \frac{3 a - b}{b - 2 a}$
199291	Simplify	fourth root of (x^12)/(y^16)	$\sqrt[4]{\frac{x^{12}}{y^{16}}}$
199292	Solve for x	(21-4x)/9+(8x+15)/3=2	$\frac{21 - 4 x}{9} + \frac{8 x + 15}{3} = 2$
199293	Evaluate the Function	x=2 : f(x)=7x-5	$x = 2$ : $f (x) = 7 x - 5$
199294	Simplify	((2a+b)/a-(a+2b)/b)*((a-b)/(b^2+ab)+(a+b)/(b^2-ab))	$(\frac{2 a + b}{a} - \frac{a + 2 b}{b}) \cdot (\frac{a - b}{b^{2} + a b} + \frac{a + b}{b^{2} - a b})$
199295	Simplify	(2a+b)/(2a^2-ab)-(16a)/(4a^2-b^2)-(2a-b)/(2a^2+ab)	$\frac{2 a + b}{2 a^{2} - a b} - \frac{16 a}{4 a^{2} - b^{2}} - \frac{2 a - b}{2 a^{2} + a b}$
199296	Rationalize the Denominator	1/( square root of 3ab)	$\frac{1}{\sqrt{3 a b}}$
199297	Factor	1/125x^3+27y^3	$\frac{1}{125} x^{3} + 27 y^{3}$
199298	Simplify	(c+6b)/(ac+2bc-6ab-3a^2)+(2b)/(a^2+2ab)-b/(ac-3a^2)	$\frac{c + 6 b}{a c + 2 b c - 6 a b - 3 a^{2}} + \frac{2 b}{a^{2} + 2 a b} - \frac{b}{a c - 3 a^{2}}$
199299	Simplify	(x-y)/x-(y-x)/y+(x^2+y^2)/(xy)	$\frac{x - y}{x} - \frac{y - x}{y} + \frac{x^{2} + y^{2}}{x y}$
199300	Solve for a	a-2/5=1/10	$a - \frac{2}{5} = \frac{1}{10}$