Solve x^2+3x-4/frac{2x-3{1-x^2}}

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

Evaluate

$$-\frac{\left(x+1\right)\left(x+4\right)\left(x-1\right)^{2}}{2x-3}$$

Short Solution Steps

Divide x^{2}+3x-4 by \frac{2x-3}{1-x^{2}} by multiplying x^{2}+3x-4 by the reciprocal of \frac{2x-3}{1-x^{2}}.

$$\frac{\left(x^{2}+3x-4\right)\left(1-x^{2}\right)}{2x-3}$$

Use the distributive property to multiply x^{2}+3x-4 by 1-x^{2} and combine like terms.

$$\frac{5x^{2}-x^{4}+3x-3x^{3}-4}{2x-3}$$

Expand

$$\frac{-x^{4}-3x^{3}+5x^{2}+3x-4}{2x-3}$$

Short Solution Steps

Divide x^{2}+3x-4 by \frac{2x-3}{1-x^{2}} by multiplying x^{2}+3x-4 by the reciprocal of \frac{2x-3}{1-x^{2}}.

$$\frac{\left(x^{2}+3x-4\right)\left(1-x^{2}\right)}{2x-3}$$

Use the distributive property to multiply x^{2}+3x-4 by 1-x^{2} and combine like terms.

$$\frac{5x^{2}-x^{4}+3x-3x^{3}-4}{2x-3}$$