Solve =(x^2+1)1/2(2x-3)^-frac{1{2}}+2x(2x-3)^frac{1{2}}

$$= ( x ^ { 2 } + 1 ) \frac { 1 } { 2 } ( 2 x - 3 ) ^ { - \frac { 1 } { 2 } } + 2 x ( 2 x - 3 ) ^ { \frac { 1 } { 2 } }$$

Factor

$$\frac{9\left(x-\frac{2-\sqrt{3}}{3}\right)\left(x-\frac{\sqrt{3}+2}{3}\right)}{2\sqrt{2x-3}}$$

Solution Steps

Use the distributive property to multiply x^{2}+1 by \frac{1}{2}.

$$factor(\left(\frac{1}{2}x^{2}+\frac{1}{2}\right)\left(2x-3\right)^{-\frac{1}{2}}+2x\left(2x-3\right)^{\frac{1}{2}})$$

Use the distributive property to multiply \frac{1}{2}x^{2}+\frac{1}{2} by \left(2x-3\right)^{-\frac{1}{2}}.

$$factor(\frac{1}{2}x^{2}\left(2x-3\right)^{-\frac{1}{2}}+\frac{1}{2}\left(2x-3\right)^{-\frac{1}{2}}+2x\left(2x-3\right)^{\frac{1}{2}})$$

Factor out \frac{1}{2}.

$$\frac{\frac{x^{2}}{\sqrt{2x-3}}+\frac{1}{\sqrt{2x-3}}+4x\sqrt{2x-3}}{2}$$

Evaluate

$$\frac{9x^{2}-12x+1}{2\sqrt{2x-3}}$$