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How do I simplify $(\frac{x \sqrt{x} - y \sqrt{y}}{x - \sqrt{x} \sqrt{y}} - \frac{x - y}{\sqrt{x} + \sqrt{y}}) \cdot {(\frac{\sqrt{x} \sqrt{y} + 2 x}{3 x})}^{- 1}$ $((xsqrt(x)-ysqrt(y))/(x-sqrt(x)sqrt(y))-(x-y)/(sqrt(x)+sqrt(y)))*((sqrt(x)sqrt(y)+2x)/(3x))^-1$ ?
How to simplify $(\sqrt{\frac{1}{x^{2}} - 1} - \frac{1}{x}) \cdot (\frac{1 - x}{\sqrt{1 - x^{2}} - 1 + x} + \frac{\sqrt{1 + x}}{\sqrt{1 + x} - \sqrt{1 - x}})$ $(sqrt [1/x^2-1]-1/x) * ((1-x) / [sqrt (1-x^2)-1+x] + sqrt(1+x) / (sqrt(1+x)-sqrt(1-x)))$ ?
How do you simplify $\frac{\frac{1}{\sqrt{a - 1}} + \sqrt{a + 1}}{\frac{1}{\sqrt{a + 1}} - \frac{1}{\sqrt{a - 1}}} \div \frac{\sqrt{a + 1}}{(a - 1) \sqrt{a + 1} - (a + 1) \sqrt{a - 1}},$ $(1/sqrt(a-1)+sqrt(a+1))/(1/sqrt(a+1)-1/sqrt(a-1))div sqrt(a+1)/((a-1)sqrt(a+1)-(a+1)sqrt(a-1)),$ a>1 ?
How to solve $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}}$ $root(3)(2+sqrt(5))+root(3)(2-sqrt(5))$ ?
How to solve $(1 - a^{2}) \div ((\frac{1 - a^{\frac{3}{2}}}{1 - a^{\frac{1}{2}}} + a^{\frac{1}{2}}) \cdot (\frac{1 + a^{\frac{3}{2}}}{1 + a^{\frac{1}{2}}} - a^{\frac{1}{2}})) + 1$ $(1-a^2)÷(((1-a^(3/2))/(1-a^(1/2))+a^(1/2))*((1+a^(3/2))/(1+a^(1/2))-a^(1/2)))+1$ , $a \geq 0, a \neq 1$ $a>=0, a≠1$ ?
What is the integral of $\int {sin}^{3} x {cos}^{2} x d x$ $int sin^3xcos^2x dx$ from $0$ $0$ to $\frac{π}{2}$ $pi/2$ ?
How to solve $3 \sqrt{ln x} + ln x = 4$ $3sqrt(lnx)+lnx=4$ ?
If $sin 2 x = 0 \Leftrightarrow x = \frac{k π}{2}$ $sin2x=0 ⇔ x=(kpi)/2$ , why isn't $sin 5 x = 0 \Leftrightarrow x = \frac{k π}{5}$ $sin5x=0 ⇔ x=(kpi)/5$ ?
How to solve $2 {cos}^{2} x + 5 cos x + 2 \geq 0$ $2cos^2x+5cosx+2>=0$ ?
How to solve $4 {sin}^{2} (\frac{3 x + π}{6}) = 3$ $4sin^2((3x+pi)/6)=3$ ?
How do I solve the equation $cot (\frac{5 π}{12} - x) + 1 = 0$ $cot({5pi}/12-x)+1=0$ ?
How do I solve $2 {sin}^{2} x - 1 = 0$ $2sin^2x-1=0$ ?
How to solve $tan (x) = \frac{cos (x) - sin (x)}{cos (x) + sin (x)}$ $tan(x)=(cos(x)-sin(x))/(cos(x)+sin(x))$ ?
How do I solve $(2 \sqrt{2} - 2) cos α = 3 {sin}^{2} α + \sqrt{2} - 4$ $(2sqrt2-2)cosalpha=3sin^2alpha+sqrt2-4$ ?
How to solve $cos (\frac{π}{4} - x) = sin (\frac{π}{6} + x)$ $cos(pi/4-x)=sin(pi/6+x)$ ?
How to solve $\frac{{sin}^{2} (α + β) - {cos}^{2} α - {cos}^{2} β}{sin (α + β) - {sin}^{2} α - {sin}^{2} β}$ $(sin^2(alpha+beta)-cos^2alpha-cos^2beta)/(sin(alpha+beta)-sin^2alpha-sin^2beta)$ if $α = \frac{π}{3}$ $alpha=pi/3$ and $β = 2 \frac{π}{3}$ $beta=2pi/3$ ?
How to solve ${(\frac{cos x + 1}{sin x})}^{2} = \frac{1}{3}$ $((cosx+1)/sinx)^2=1/3$ ?
How to solve $1 + 2 {cos}^{2} (x + \frac{π}{6}) = 3 sin (\frac{π}{3} - x)$ $1+2cos^2(x+pi/6)=3sin(pi/3-x)$ ?
How to solve $sin 3 x < sin x$ $sin3x<sinx$ ?
How to solve $t g^{2} x - (1 + \sqrt{3}) t g x + \sqrt{3} < 0$ $tg^2x-(1+sqrt3)tgx+sqrt3<0$ ?
How do I solve $sin x - \sqrt{3} sin 3 x + sin 5 x < 0$ $sinx-sqrt3sin3x+sin5x<0$ ?