Solve 1/5(frac{1{-8x-10})+2}

$$\frac { 1 } { 5 ( \frac { 1 } { - 8 x - 10 } ) + 2 }$$

Evaluate

$$\frac{2\left(4x+5\right)}{16x+15}$$

Short Solution Steps

Express 5\times \frac{1}{-8x-10} as a single fraction.

$$\frac{1}{\frac{5}{-8x-10}+2}$$

Factor -8x-10.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2\left(-4x-5\right)}{2\left(-4x-5\right)}.

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

Since \frac{5}{2\left(-4x-5\right)} and \frac{2\times 2\left(-4x-5\right)}{2\left(-4x-5\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 5+2\times 2\left(-4x-5\right).

$$\frac{1}{\frac{5-16x-20}{2\left(-4x-5\right)}}$$

Combine like terms in 5-16x-20.

$$\frac{1}{\frac{-15-16x}{2\left(-4x-5\right)}}$$

Divide 1 by \frac{-15-16x}{2\left(-4x-5\right)} by multiplying 1 by the reciprocal of \frac{-15-16x}{2\left(-4x-5\right)}.

$$\frac{2\left(-4x-5\right)}{-15-16x}$$

Use the distributive property to multiply 2 by -4x-5.

$$\frac{-8x-10}{-15-16x}$$

Factor

$$\frac{2\left(4x+5\right)}{16x+15}$$