Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
101	Solve for a	(4a-4)/16-(3-5a)/24=1	$\frac{4 a - 4}{16} - \frac{3 - 5 a}{24} = 1$
102	Solve the Inequality for x	((x-12)(x+5))/((x-3)^3)<=0	$\frac{(x - 12) (x + 5)}{{(x - 3)}^{3}} \leq 0$
103	Evaluate	((3/5)(2/5))÷(4/7)	$((\frac{3}{5}) (\frac{2}{5})) \div \frac{4}{7}$
104	Evaluate	(1/2+1/3+1/6)÷2 1/2	$(\frac{1}{2} + \frac{1}{3} + \frac{1}{6}) \div 2 \frac{1}{2}$
105	Solve for x	(x+4)^2-2x-5=(x-1)^2	${(x + 4)}^{2} - 2 x - 5 = {(x - 1)}^{2}$
106	Solve the Inequality for x	7 square root of x+1<9	$7 \sqrt{x} + 1 < 9$
107	Simplify	(6^(1/2)*4^(1/3))^2	${(6^{\frac{1}{2}} \cdot 4^{\frac{1}{3}})}^{2}$
108	Write in Exponential Form	2 square root of a+3 square root of b	$2 \sqrt{a} + 3 \sqrt{b}$
109	Solve for x	(5-x)^(1/2)-2x=0	${(5 - x)}^{\frac{1}{2}} - 2 x = 0$
110	Graph Using a Table of Values	Y=(1/4)^x	$Y = {(\frac{1}{4})}^{x}$
111	Find the Antiderivative	f(x)=-3x^-4+10x^(2/3)-7x	$f (x) = - 3 x^{- 4} + 10 x^{\frac{2}{3}} - 7 x$
112	Simplify	-9m^-2n^5*2m^-3n^-6	$- 9 m^{- 2} n^{5} \cdot 2 m^{- 3} n^{- 6}$
113	Simplify	(y*y^(1/3))^(3/2)	${(y \cdot y^{\frac{1}{3}})}^{\frac{3}{2}}$
114	Find the Antiderivative	f(x)=3x+8x^3+x^-3+5x^2	$f (x) = 3 x + 8 x^{3} + x^{- 3} + 5 x^{2}$
115	Simplify	(6w^3+7w^2-12w+15)/(2w^2+3w-5)	$\frac{6 w^{3} + 7 w^{2} - 12 w + 15}{2 w^{2} + 3 w - 5}$
116	Factor	mn-mk+xk-xn	$m n - m k + x k - x n$
117	Simplify	12 root of 729	$\sqrt[12]{729}$
118	Simplify	(4-x)/(x^2-3x)-(2x+7)/(x^2-6x+9)	$\frac{4 - x}{x^{2} - 3 x} - \frac{2 x + 7}{x^{2} - 6 x + 9}$
119	Simplify	((2ab)/(a^2-b^2))÷((4ab)/((a-b)^2))	$\frac{2 a b}{a^{2} - b^{2}} \div \frac{4 a b}{{(a - b)}^{2}}$
120	Simplify the Radical Expression	square root of (27x^4)/(75y^2)	$\sqrt{\frac{27 x^{4}}{75 y^{2}}}$
121	Solve for z	5/3z+1=3-2/3Z	$\frac{5}{3} z + 1 = 3 - \frac{2}{3} Z$
122	Simplify	((2a+3b)/(2a)+(2a-3b)/(3b))^2-((2a+3b)/(2a)-(2a-3b)/(3b))^2	${(\frac{2 a + 3 b}{2 a} + \frac{2 a - 3 b}{3 b})}^{2} - {(\frac{2 a + 3 b}{2 a} - \frac{2 a - 3 b}{3 b})}^{2}$
123	Solve for x	(8x+7)/6+(3-2x)/4-(5x-2)/2=32	$\frac{8 x + 7}{6} + \frac{3 - 2 x}{4} - \frac{5 x - 2}{2} = 32$
124	Find the Roots (Zeros)	9x^2-1-(3x-2)^2=0	$9 x^{2} - 1 - {(3 x - 2)}^{2} = 0$
125	Simplify	(8-x^3)/(25x^2+100-100x)	$\frac{8 - x^{3}}{25 x^{2} + 100 - 100 x}$
126	Evaluate the Limit	limit as x approaches infinity of (2x+3)/(5x^2+4)	$lim_{x \to \infty} \frac{2 x + 3}{5 x^{2} + 4}$
127	Solve for x	6.2÷(2x+1)=2 1/3÷4	$6.2 \div (2 x + 1) = 2 \frac{1}{3} \div 4$
128	Solve for x	(2x-5.6)/3=(1-x)/1.5	$\frac{2 x - 5.6}{3} = \frac{1 - x}{1.5}$
129	Solve for z	square root of (z+5)^2=6	$\sqrt{{(z + 5)}^{2}} = 6$
130	Simplify	( square root of 2+ square root of 5)/( square root of 2- square root of 5)	$\frac{\sqrt{2} + \sqrt{5}}{\sqrt{2} - \sqrt{5}}$
131	Factor	f(x)=64x^3-240x^2+300x-125	$f (x) = 64 x^{3} - 240 x^{2} + 300 x - 125$
132	Simplify	(x^2+3x+2)/(x(x+2)^3(x+1))-1/(x(x+2)(x+5))	$\frac{x^{2} + 3 x + 2}{x {(x + 2)}^{3} (x + 1)} - \frac{1}{x (x + 2) (x + 5)}$
133	Simplify	cube root of square root of 64	$\sqrt[3]{\sqrt[2]{64}}$
134	Solve for x	64^(x+1)=32^(6/5x)	$64^{x + 1} = 32^{\frac{6}{5} x}$
135	Simplify	(1/x)^0	${(\frac{1}{x})}^{0}$
136	Solve for x	7 square root of x+1<9	$7 \sqrt{x} + 1 < 9$
137	Simplify the Radical Expression	cube root of square root of 64	$\sqrt[3]{\sqrt{64}}$
138	Rationalize the Denominator	square root of (2x)/y	$\sqrt{\frac{2 x}{y}}$
139	Simplify	(x+y)/(2xy-y^2)-(x-y)/(2x^2-xy)	$\frac{x + y}{2 x y - y^{2}} - \frac{x - y}{2 x^{2} - x y}$
140	Simplify	square root of 2x^4* square root of 8x^3	$\sqrt{2 x^{4}} \cdot \sqrt{8 x^{3}}$
141	Simplify	cube root of square root of 27	$\sqrt[3]{\sqrt{27}}$
142	Solve for y	2xy+6y=10	$2 x y + 6 y = 10$
143	Solve for x	square root of 2x-2/3=0	$\sqrt{2 x} - \frac{2}{3} = 0$
144	Graph	y> = square root of x-2+1	$y \geq \sqrt{x - 2} + 1$
145	Solve for n	1+2cot(theta)^2+cot(theta)^4=csc(theta)^n	$1 + 2 \cot^{2} (θ) + \cot^{4} (θ) = {\csc (θ)}^{n}$
146	Solve for z	2/y=x/(3z)	$\frac{2}{y} = \frac{x}{3 z}$
147	Solve for y	x-1/3y=-1	$x - \frac{1}{3} y = - 1$
148	Solve for k	cube root of k+4 = cube root of 2k+3	$\sqrt[3]{k + 4} = \sqrt[3]{2 k + 3}$
149	Find the Derivative - d/dx	y=sin(4x)-8x^2+9x+pi	$y = \sin (4 x) - 8 x^{2} + 9 x + π$
150	Solve the System of Inequalities	y<=-3x+1 y>=-1/4x+6	$y \leq - 3 x + 1$ $y \geq - \frac{1}{4} x + 6$
151	Simplify	((2x^3)^2(3y^4)^3)/(12x^4y^5)-4x^2y^7	$\frac{{(2 x^{3})}^{2} {(3 y^{4})}^{3}}{12 x^{4} y^{5}} - 4 x^{2} y^{7}$
152	Simplify	( cube root of 625x^6y^4)/( cube root of 5xy)	$\frac{\sqrt[3]{625 x^{6} y^{4}}}{\sqrt[3]{5 x y}}$
153	Evaluate the Limit	limit as x approaches pi/4 of (tan(x))/x	$lim_{x \to \frac{π}{4}} \frac{\tan (x)}{x}$
154	Simplify	(1+i square root of 2)/2-(1-i square root of 1/2)	$\frac{(1 + i \sqrt{2})}{2} - (1 - i \sqrt{\frac{1}{2}})$
155	Factor	(b-c)^3+(c-a)^3+(a-b)^3	${(b - c)}^{3} + {(c - a)}^{3} + {(a - b)}^{3}$
156	Find the Product	(3a-b+2c)^2	${(3 a - b + 2 c)}^{2}$
157	Simplify the Radical Expression	5/(3- square root of 2)	$\frac{5}{3 - \sqrt{2}}$
158	Simplify	(a^2-b^2)/(a^2-a+ab-b)	$\frac{a^{2} - b^{2}}{a^{2} - a + a b - b}$
159	Solve for t	7/12t-1/4=5/6	$\frac{7}{12} t - \frac{1}{4} = \frac{5}{6}$
160	Simplify	(mx+my)/(5n)*(10m)/(ny+nx)	$\frac{m x + m y}{5 n} \cdot \frac{10 m}{n y + n x}$
161	Evaluate the Integral	integral of (x+1)(x+a) with respect to x	$\int (x + 1) (x + a) d x$
162	Solve the Inequality for x	(x+3)/((x-4)^2(x^2-4))<=0	$\frac{x + 3}{{(x - 4)}^{2} (x^{2} - 4)} \leq 0$
163	Evaluate	(2^-2m^-3)/(n^0)	$\frac{2^{- 2} m^{- 3}}{n^{0}}$
164	Solve for y	1/3y=2/3y^2	$\frac{1}{3} y = \frac{2}{3} y^{2}$
165	Simplify	(30c^2+19ac-63a^2)/(6c-7a)	$\frac{30 c^{2} + 19 a c - 63 a^{2}}{6 c - 7 a}$
166	Solve for x	2x^2(x-1)=0	$2 x^{2} (x - 1) = 0$
167	Simplify	3(5-12)+4÷2	$3 (5 - 12) + 4 \div 2$
168	Simplify	-3xy(x^3y^3-3x^2y+7xy^2)	$- 3 x y (x^{3} y^{3} - 3 x^{2} y + 7 x y^{2})$
169	Evaluate	(s^-5)^3	${(s^{- 5})}^{3}$
170	Simplify the Radical Expression	square root of cube root of 64	$\sqrt{\sqrt[3]{64}}$
171	Simplify	17(a^(2n+1))^42a^(7n-12)	$17 \cdot {(a^{2 n + 1})}^{4} \cdot 2 a^{7 n - 12}$
172	Solve for x	3.4/(2x-12)=18/4.5	$\frac{3.4}{2 x - 12} = \frac{18}{4.5}$
173	Divide	( cube root of 48x^3y^7)/( cube root of 8x^5y)	$\frac{\sqrt[3]{48 x^{3} y^{7}}}{\sqrt[3]{8 x^{5} y}}$
174	Evaluate the Integral	integral of (x-1)(x+a) with respect to x	$\int (x - 1) (x + a) d x$
175	Simplify	(36x^4y^5)/((3xy)^2)	$\frac{36 x^{4} y^{5}}{{(3 x y)}^{2}}$
176	Simplify	(16a^4+16a)/(a^2+1-a)	$\frac{16 a^{4} + 16 a}{a^{2} + 1 - a}$
177	Solve the Rational Equation for x	square root of x=9	$\sqrt{x} = 9$
178	Simplify	(x^16y^20z^8)^(1/4)	${(x^{16} y^{20} z^{8})}^{\frac{1}{4}}$
179	Simplify	(x^2-1)/(5xy)*(x^2y)/(1+x)	$\frac{x^{2} - 1}{5 x y} \cdot \frac{x^{2} y}{1 + x}$
180	Simplify	((3m^2n^3)/(xy^2))^2((x^3yz^2)/(2mn^2))^3	${(\frac{3 m^{2} n^{3}}{x y^{2}})}^{2} {(\frac{x^{3} y z^{2}}{2 m n^{2}})}^{3}$
181	Simplify	15 root of x^10b^15	$\sqrt[15]{x^{10} b^{15}}$
182	Simplify	(25a^5b^3c)/(5ab^4c)	$\frac{25 a^{5} b^{3} c}{5 a b^{4} c}$
183	Simplify	(5 square root of 3+ square root of 15)*(3 square root of 5- square root of 15)	$(5 \sqrt{3} + \sqrt{15}) \cdot (3 \sqrt{5} - \sqrt{15})$
184	Solve for θ	-2cos(theta)^2+sin(theta)+1=0	$- 2 \cos^{2} (θ) + \sin (θ) + 1 = 0$
185	Simplify	13(8^(3/4))-4*8^(3/4)	$13 (8^{\frac{3}{4}}) - 4 \cdot 8^{\frac{3}{4}}$
186	Simplify	( square root of 3- square root of 6+ square root of 12- square root of 24)*( square root of 6)/2	$(\sqrt{3} - \sqrt{6} + \sqrt{12} - \sqrt{24}) \cdot \frac{\sqrt{6}}{2}$
187	Solve for z	(2z-3)/5-(z-6)/4=3	$\frac{2 z - 3}{5} - \frac{z - 6}{4} = 3$
188	Factor	2x-4xy+10y-5	$2 x - 4 x y + 10 y - 5$
189	Simplify	(2b)/(2b+3)+5/(3-2b)-(4b^2+9)/(4b^2-9)	$\frac{2 b}{2 b + 3} + \frac{5}{3 - 2 b} - \frac{4 b^{2} + 9}{4 b^{2} - 9}$
190	Simplify the Radical Expression	( square root of 2+ square root of 5)/( square root of 2- square root of 5)	$\frac{\sqrt{2} + \sqrt{5}}{\sqrt{2} - \sqrt{5}}$
191	Solve for x	(3x-4b)+(7b+2x)=13b	$(3 x - 4 b) + (7 b + 2 x) = 13 b$
192	Solve for x	4x(5x+7)=4(5x^2+8x+4)	$4 x (5 x + 7) = 4 (5 x^{2} + 8 x + 4)$
193	Simplify	(a-2y)/(a+y)-(y^2-5ay)/(a^2-y^2)	$\frac{a - 2 y}{a + y} - \frac{y^{2} - 5 a y}{a^{2} - y^{2}}$
194	Simplify	(5^(1/2)*5^(-3/2))^(-1/4)	${(5^{\frac{1}{2}} \cdot 5^{- \frac{3}{2}})}^{- \frac{1}{4}}$
195	Evaluate	(5/8-1/3)÷(2/5+1)	$(\frac{5}{8} - \frac{1}{3}) \div (\frac{2}{5} + 1)$
196	Simplify	8-5y+2x-3+4y+2+4x-2	$8 - 5 y + 2 x - 3 + 4 y + 2 + 4 x - 2$
197	Simplify	5(x^(2n-1))*(2x^(3n+1))^2	$5 (x^{2 n - 1}) \cdot {(2 x^{3 n + 1})}^{2}$
198	Rationalize the Denominator	(4- square root of 5)/( square root of 5)	$\frac{4 - \sqrt{5}}{\sqrt{5}}$
199	Solve for x	2/y=x/(3z)	$\frac{2}{y} = \frac{x}{3 z}$
200	Verify the Identity	1+x+(x^2)/(1-x)=1/(1-x)	$1 + x + \frac{x^{2}}{1 - x} = \frac{1}{1 - x}$