Solve 2x^2+8x-10/2x^2+15x+25div4x^2+20x-24/2x^2+x-10

$$\frac { 2 x ^ { 2 } + 8 x - 10 } { 2 x ^ { 2 } + 15 x + 25 } \div \frac { 4 x ^ { 2 } + 20 x - 24 } { 2 x ^ { 2 } + x - 10 }$$

Evaluate

$$\frac{x-2}{2\left(x+6\right)}$$

Short Solution Steps

Divide \frac{2x^{2}+8x-10}{2x^{2}+15x+25} by \frac{4x^{2}+20x-24}{2x^{2}+x-10} by multiplying \frac{2x^{2}+8x-10}{2x^{2}+15x+25} by the reciprocal of \frac{4x^{2}+20x-24}{2x^{2}+x-10}.

$$\frac{\left(2x^{2}+8x-10\right)\left(2x^{2}+x-10\right)}{\left(2x^{2}+15x+25\right)\left(4x^{2}+20x-24\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(x-2\right)\left(x-1\right)\left(x+5\right)\left(2x+5\right)}{4\left(x-1\right)\left(x+5\right)\left(x+6\right)\left(2x+5\right)}$$

Cancel out 2\left(x-1\right)\left(x+5\right)\left(2x+5\right) in both numerator and denominator.

$$\frac{x-2}{2\left(x+6\right)}$$

Expand the expression.

$$\frac{x-2}{2x+12}$$

Expand

$$\frac{x-2}{2\left(x+6\right)}$$

Short Solution Steps

Divide \frac{2x^{2}+8x-10}{2x^{2}+15x+25} by \frac{4x^{2}+20x-24}{2x^{2}+x-10} by multiplying \frac{2x^{2}+8x-10}{2x^{2}+15x+25} by the reciprocal of \frac{4x^{2}+20x-24}{2x^{2}+x-10}.

$$\frac{\left(2x^{2}+8x-10\right)\left(2x^{2}+x-10\right)}{\left(2x^{2}+15x+25\right)\left(4x^{2}+20x-24\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(x-2\right)\left(x-1\right)\left(x+5\right)\left(2x+5\right)}{4\left(x-1\right)\left(x+5\right)\left(x+6\right)\left(2x+5\right)}$$

Cancel out 2\left(x-1\right)\left(x+5\right)\left(2x+5\right) in both numerator and denominator.

$$\frac{x-2}{2\left(x+6\right)}$$

Expand the expression.

$$\frac{x-2}{2x+12}$$