Solve 1/5-2(x+h)-1/5-2x

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

Evaluate

$$\frac{2h}{\left(5-2x\right)\left(5-2h-2x\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5-2\left(x+h\right) and 5-2x is \left(-2x+5\right)\left(-2\left(x+h\right)+5\right). Multiply \frac{1}{5-2\left(x+h\right)} times \frac{-2x+5}{-2x+5}. Multiply \frac{1}{5-2x} times \frac{-2\left(x+h\right)+5}{-2\left(x+h\right)+5}.

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

Since \frac{-2x+5}{\left(-2x+5\right)\left(-2\left(x+h\right)+5\right)} and \frac{-2\left(x+h\right)+5}{\left(-2x+5\right)\left(-2\left(x+h\right)+5\right)} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Combine like terms in -2x+5+2x+2h-5.

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

Expand \left(-2x+5\right)\left(-2\left(x+h\right)+5\right).

$$\frac{2h}{4x^{2}+4hx-20x-10h+25}$$

Expand

$$\frac{2h}{\left(5-2x\right)\left(5-2h-2x\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5-2\left(x+h\right) and 5-2x is \left(-2x+5\right)\left(-2\left(x+h\right)+5\right). Multiply \frac{1}{5-2\left(x+h\right)} times \frac{-2x+5}{-2x+5}. Multiply \frac{1}{5-2x} times \frac{-2\left(x+h\right)+5}{-2\left(x+h\right)+5}.

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

Since \frac{-2x+5}{\left(-2x+5\right)\left(-2\left(x+h\right)+5\right)} and \frac{-2\left(x+h\right)+5}{\left(-2x+5\right)\left(-2\left(x+h\right)+5\right)} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Combine like terms in -2x+5+2x+2h-5.

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

Expand \left(-2x+5\right)\left(-2\left(x+h\right)+5\right).

$$\frac{2h}{4x^{2}+4hx-20x-10h+25}$$