Solve 4x^2+6x/1-5x*10x^2+13x-3/6x-4x^2

$$\frac { 4 x ^ { 2 } + 6 x } { 1 - 5 x } \times \frac { 10 x ^ { 2 } + 13 x - 3 } { 6 x - 4 x ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Multiply \frac{4x^{2}+6x}{1-5x} times \frac{10x^{2}+13x-3}{6x-4x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4x^{2}+6x\right)\left(10x^{2}+13x-3\right)}{\left(1-5x\right)\left(6x-4x^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{2x\left(5x-1\right)\left(2x+3\right)^{2}}{2x\left(-5x+1\right)\left(-2x+3\right)}$$

Extract the negative sign in -1+5x.

$$\frac{-2x\left(-5x+1\right)\left(2x+3\right)^{2}}{2x\left(-5x+1\right)\left(-2x+3\right)}$$

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

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

Expand the expression.

$$\frac{-4x^{2}-12x-9}{-2x+3}$$

Expand

$$\frac{4x^{2}+12x+9}{2x-3}$$

Short Solution Steps

Multiply \frac{4x^{2}+6x}{1-5x} times \frac{10x^{2}+13x-3}{6x-4x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4x^{2}+6x\right)\left(10x^{2}+13x-3\right)}{\left(1-5x\right)\left(6x-4x^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{2x\left(5x-1\right)\left(2x+3\right)^{2}}{2x\left(-5x+1\right)\left(-2x+3\right)}$$

Extract the negative sign in -1+5x.

$$\frac{-2x\left(-5x+1\right)\left(2x+3\right)^{2}}{2x\left(-5x+1\right)\left(-2x+3\right)}$$

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

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

Expand the expression.

$$\frac{-4x^{2}-12x-9}{-2x+3}$$