Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
10901	Simplify	((t+1)(t^2-1))/((t-1)(t+1)^2)	$\frac{(t + 1) (t^{2} - 1)}{(t - 1) {(t + 1)}^{2}}$
10902	Simplify	( square root of 14(cos(120)+i*sin(120)))^4	${(\sqrt{14} (\cos (120) + i \cdot \sin (120)))}^{4}$
10903	Simplify	( square root of 14(cos(85)+isin(85)))^6	${(\sqrt{14} (\cos (85) + i \sin (85)))}^{6}$
10904	Simplify	((b^(2n+1))^3)/(b^n*b^(4n+3))	$\frac{{(b^{2 n + 1})}^{3}}{b^{n} \cdot b^{4 n + 3}}$
10905	Simplify	(5x^2+11x+2)/(x+2)	$\frac{5 x^{2} + 11 x + 2}{x + 2}$
10906	Simplify	((-9 square root of 3-9i)(9-9 square root of 3i))/((9+9 square root of 3i)(9+9 square root of 3i))	$\frac{(- 9 \sqrt{3} - 9 i) \cdot (9 - 9 \sqrt{3} i)}{(9 + 9 \sqrt{3} i) \cdot (9 + 9 \sqrt{3} i)}$
10907	Simplify	(3 square root of 3+3i)^5	${(3 \sqrt{3} + 3 i)}^{5}$
10908	Simplify	(6x^3+17x^2+27x+20)/(3x+4)	$\frac{6 x^{3} + 17 x^{2} + 27 x + 20}{3 x + 4}$
10909	Simplify	((2x-3)^2)/(x^3-x^2+4x-5)	$\frac{{(2 x - 3)}^{2}}{x^{3} - x^{2} + 4 x - 5}$
10910	Simplify	((a^3*b^2)^5)/(ab)	$\frac{{(a^{3} \cdot b^{2})}^{5}}{a b}$
10911	Simplify	((2p)/3)/4	$\frac{\frac{2 p}{3}}{4}$
10912	Simplify	((p^2+20+100)/(p^2-5p-50))/((p^2-100)/7)	$\frac{\frac{p^{2} + 20 + 100}{p^{2} - 5 p - 50}}{\frac{p^{2} - 100}{7}}$
10913	Simplify	((35/(x-3))/21)/x	$\frac{\frac{\frac{35}{x - 3}}{21}}{x}$
10914	Simplify	(1/6)/(( square root of 35)/6)	$\frac{\frac{1}{6}}{\frac{\sqrt{35}}{6}}$
10915	Simplify	( square root of 1-1/2)/2	$\frac{\sqrt{1 - \frac{1}{2}}}{2}$
10916	Simplify	( square root of 108x^5)/( square root of 3x)	$\frac{\sqrt{108 x^{5}}}{\sqrt{3 x}}$
10917	Simplify	(pi-2pi+3pi-4pi)/pi	$\frac{π - 2 π + 3 π - 4 π}{π}$
10918	Simplify	( square root of 1-cos(6x))/2	$\frac{\sqrt{1 - \cos (6 x)}}{2}$
10919	Simplify	( square root of 100x^4y^2)/(2 square root of 25x^2y)	$\frac{\sqrt{100 x^{4} y^{2}}}{2 \sqrt{25 x^{2} y}}$
10920	Simplify	( square root of 1-cos(30/2))/2	$\frac{\sqrt{1 - \cos (\frac{30}{2})}}{2}$
10921	Simplify	( square root of 29)/5	$\frac{\sqrt{29}}{5}$
10922	Simplify	( square root of 3- square root of 5)/( square root of 15- square root of 14)	$\frac{\sqrt{3} - \sqrt{5}}{\sqrt{15} - \sqrt{14}}$
10923	Simplify	((4y^2-9)/(2y^2+9y-18))/((2y^2+y-3)/(y^2+5y-6))	$\frac{\frac{4 y^{2} - 9}{2 y^{2} + 9 y - 18}}{\frac{2 y^{2} + y - 3}{y^{2} + 5 y - 6}}$
10924	Simplify	(k^2-4k-21)/(k^2+9k+18)	$\frac{k^{2} - 4 k - 21}{k^{2} + 9 k + 18}$
10925	Simplify	(10^x+10^(-x))/(10^x-10^(-x))=5	$\frac{10^{x} + 10^{- x}}{10^{x} - 10^{- x}} = 5$
10926	Simplify	((3x^2+12x-15)/(x^2+2x-15))/((3x^2-3x)/(3x-x^2))	$\frac{\frac{3 x^{2} + 12 x - 15}{x^{2} + 2 x - 15}}{\frac{3 x^{2} - 3 x}{3 x - x^{2}}}$
10927	Simplify	((3pi)/4)/8	$\frac{\frac{3 π}{4}}{8}$
10928	Simplify	(3/4)/(( square root of 7)/4)	$\frac{\frac{3}{4}}{\frac{\sqrt{7}}{4}}$
10929	Simplify	( square root of 2-i)^6	${(\sqrt{2} - i)}^{6}$
10930	Simplify	( square root of 2+i square root of 2)^3	${(\sqrt{2} + i \sqrt{2})}^{3}$
10931	Simplify	(7 square root of 10+7)(6 square root of 10-4 square root of 7)	$(7 \sqrt{10} + 7) (6 \sqrt{10} - 4 \sqrt{7})$
10932	Simplify	( eighth root of y^7)( cube root of y^2)	$(\sqrt[8]{y^{7}}) (\sqrt[3]{y^{2}})$
10933	Simplify	( square root of 2(cos((7pi)/6)+isin((7pi)/6)))^4	${(\sqrt{2} (\cos (\frac{7 π}{6}) + i \sin (\frac{7 π}{6})))}^{4}$
10934	Simplify	( square root of 3-i)^6	${(\sqrt{3} - i)}^{6}$
10935	Simplify	( square root of x- square root of y)( square root of x- square root of y)	$(\sqrt{x} - \sqrt{y}) (\sqrt{x} - \sqrt{y})$
10936	Simplify	( square root of 2)^4(cos(4120)+isin(4120))	${(\sqrt{2})}^{4} (\cos (4 \cdot 120) + i \sin (4 \cdot 120))$
10937	Simplify	((x^2-9x+3)+h-x^2-9x+3)/h	$\frac{(x^{2} - 9 x + 3) + h - x^{2} - 9 x + 3}{h}$
10938	Simplify	(1- square root of 3i)^7	${(1 - \sqrt{3} i)}^{7}$
10939	Simplify	(x^4-5x^3+7x-12)/(x-4)	$\frac{x^{4} - 5 x^{3} + 7 x - 12}{x - 4}$
10940	Simplify	(x^2-3x-28)/(x^2-16)	$\frac{x^{2} - 3 x - 28}{x^{2} - 16}$
10941	Simplify	( square root of 4cos(45))( square root of 4cos(135))	$(\sqrt{4} \cos (45)) (\sqrt{4} \cos (135))$
10942	Simplify	((2x-1)/(x+1))( square root of x)	$(\frac{2 x - 1}{x + 1}) (\sqrt{x})$
10943	Simplify	( square root of 2+2i)( square root of 2-2i)	$(\sqrt{2} + 2 i) (\sqrt{2} - 2 i)$
10944	Simplify	( square root of 2+3i)( square root of 2-3i)	$(\sqrt{2} + 3 i) (\sqrt{2} - 3 i)$
10945	Simplify	(1+i square root of 3)(1+i)	$(1 + i \sqrt{3}) (1 + i)$
10946	Simplify	( cube root of 27x^2)( cube root of 16x^4)	$(\sqrt[3]{27 x^{2}}) (\sqrt[3]{16 x^{4}})$
10947	Simplify	(1/2-4/d)/(1/d+3/(2d))	$\frac{\frac{1}{2} - \frac{4}{d}}{\frac{1}{d} + \frac{3}{2 d}}$
10948	Simplify	(( square root of 6)/4-( square root of 2)/4)^2	${(\frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4})}^{2}$
10949	Simplify	(( square root of 6)^( square root of 2))^2	${({(\sqrt{6})}^{\sqrt{2}})}^{2}$
10950	Simplify	(4m^2)/(4m^2)	$\frac{4 m^{2}}{4 m^{2}}$
10951	Simplify	(3-5x)/((x+3)(x-3))	$\frac{3 - 5 x}{(x + 3) (x - 3)}$
10952	Simplify	3/( square root of 3x^2y)	$\frac{3}{\sqrt{3 x^{2} y}}$
10953	Simplify	(40i)/(3+i)	$\frac{40 i}{3 + i}$
10954	Simplify	(450p+900)/(1350+900 square root of 2)	$\frac{450 p + 900}{1350 + 900 \sqrt{2}}$
10955	Simplify	(4pi)/(2pi)	$\frac{4 π}{2 π}$
10956	Simplify	(5p^2+20p+15)/(25p^2-50p-75)	$\frac{5 p^{2} + 20 p + 15}{25 p^{2} - 50 p - 75}$
10957	Simplify	7/(13 square root of 2)	$\frac{7}{13 \sqrt{2}}$
10958	Simplify	(5-x)/(x^2-25)	$\frac{5 - x}{x^{2} - 25}$
10959	Simplify	6/( square root of 14)	$\frac{6}{\sqrt{14}}$
10960	Simplify	(75pi)/180	$\frac{75 π}{180}$
10961	Simplify	6/(4 square root of 3)	$\frac{6}{4 \sqrt{3}}$
10962	Simplify	(6t-6)/(t^2-1)	$\frac{6 t - 6}{t^{2} - 1}$
10963	Simplify	(5 square root of 2)/(tan(45))	$\frac{5 \sqrt{2}}{\tan (45)}$
10964	Simplify	5/( square root of 34)	$\frac{5}{\sqrt{34}}$
10965	Simplify	(5pi)/18	$\frac{5 π}{18}$
10966	Simplify	(5m^9+15m^5+40m)/(10m)	$\frac{5 m^{9} + 15 m^{5} + 40 m}{10 m}$
10967	Simplify	(5t-10)/(t^2-4)	$\frac{5 t - 10}{t^{2} - 4}$
10968	Simplify	(2sin(x))/( square root of 3)	$\frac{2 \sin (x)}{\sqrt{3}}$
10969	Simplify	(2pi)/(pi/5)	$\frac{2 π}{\frac{π}{5}}$
10970	Simplify	(2pi)/(1/5*pi)	$\frac{2 π}{\frac{1}{5} \cdot π}$
10971	Simplify	(2pi)/(2/5)	$\frac{2 π}{\frac{2}{5}}$
10972	Simplify	(2pi)/((2pi)/7)	$\frac{2 π}{\frac{2 π}{7}}$
10973	Simplify	(2pi)/(3/4)	$\frac{2 π}{\frac{3}{4}}$
10974	Simplify	(2pi)/((4pi)/9)	$\frac{2 π}{\frac{4 π}{9}}$
10975	Simplify	(-27x^5+60x^6)/(15x^6)	$\frac{- 27 x^{5} + 60 x^{6}}{15 x^{6}}$
10976	Simplify	2/(a/(2/b))	$\frac{2}{\frac{a}{\frac{2}{b}}}$
10977	Simplify	-2/(2 square root of 3)	$\frac{- 2}{2 \sqrt{3}}$
10978	Simplify	2/( square root of 10)	$\frac{2}{\sqrt{10}}$
10979	Simplify	(2x^3y^3+8xy+x^2y^2)/(2xy)	$\frac{2 x^{3} y^{3} + 8 x y + x^{2} y^{2}}{2 x y}$
10980	Simplify	(2x^2-12x)/(x-6)	$\frac{2 x^{2} - 12 x}{x - 6}$
10981	Simplify	(19pi)/90	$\frac{19 π}{90}$
10982	Simplify	((2(4x-3))/(2-x)+3)/((4x-3)/(2-x)+4)	$\frac{\frac{2 (4 x - 3)}{2 - x} + 3}{\frac{4 x - 3}{2 - x} + 4}$
10983	Simplify	(17pi)/12	$\frac{17 π}{12}$
10984	Simplify	(x^2+x-6)/(x^2-x-6)	$\frac{x^{2} + x - 6}{x^{2} - x - 6}$
10985	Simplify	(x^-1y^4)/(3x^-5y-1)	$\frac{x^{- 1} y^{4}}{3 x^{- 5} y - 1}$
10986	Simplify	( cube root of -162m^6)/( cube root of 3m^-3)	$\frac{\sqrt[3]{- 162 m^{6}}}{\sqrt[3]{3 m^{- 3}}}$
10987	Simplify	( cube root of 125x^5y^6)/27	$\frac{\sqrt[3]{125 x^{5} y^{6}}}{27}$
10988	Simplify	(x/10-1/10-2/x)/(1/2-x/10)	$\frac{\frac{x}{10} - \frac{1}{10} - \frac{2}{x}}{\frac{1}{2} - \frac{x}{10}}$
10989	Simplify	( square root of 3-2x- square root of 3x)/x	$\frac{\sqrt{3 - 2 x} - \sqrt{3 x}}{x}$
10990	Simplify	( square root of 7)/( square root of 21)	$\frac{\sqrt{7}}{\sqrt{21}}$
10991	Simplify	( square root of -64)/( square root of 2)	$\frac{\sqrt{- 64}}{\sqrt{2}}$
10992	Simplify	( cube root of a^6b^9)/-64	$\frac{\sqrt[3]{a^{6} b^{9}}}{- 64}$
10993	Simplify	( square root of 3)/2m	$\frac{\sqrt{3}}{2} m$
10994	Simplify	( square root of 58)/3	$\frac{\sqrt{58}}{3}$
10995	Simplify	(- square root of 3-3-1- square root of 3)/(1-3)	$\frac{- \sqrt{3} - 3 - 1 - \sqrt{3}}{1 - 3}$
10996	Simplify	-( square root of 5)/10	$- \frac{\sqrt{5}}{10}$
10997	Simplify	( square root of 34)/6	$\frac{\sqrt{34}}{6}$
10998	Simplify	( square root of 40x^5)/( square root of 10x)	$\frac{\sqrt{40 x^{5}}}{\sqrt{10 x}}$
10999	Simplify	(10 square root of 3)/(sin(60))	$\frac{10 \sqrt{3}}{\sin (60)}$
11000	Simplify	(10d)/(15d-20d^2)	$\frac{10 d}{15 d - 20 d^{2}}$