Solve h(x)=-2/(x-5)^2+10

$$h ( x ) = \frac { - 2 } { ( x - 5 ) ^ { 2 } } + 10$$

Evaluate

$$\frac{2\left(5x^{2}-50x+124\right)}{\left(x-5\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times \frac{\left(x-5\right)^{2}}{\left(x-5\right)^{2}}.

$$\frac{-2}{\left(x-5\right)^{2}}+\frac{10\left(x-5\right)^{2}}{\left(x-5\right)^{2}}$$

Since \frac{-2}{\left(x-5\right)^{2}} and \frac{10\left(x-5\right)^{2}}{\left(x-5\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{-2+10\left(x-5\right)^{2}}{\left(x-5\right)^{2}}$$

Do the multiplications in -2+10\left(x-5\right)^{2}.

$$\frac{-2+10x^{2}-100x+250}{\left(x-5\right)^{2}}$$

Combine like terms in -2+10x^{2}-100x+250.

$$\frac{248+10x^{2}-100x}{\left(x-5\right)^{2}}$$

Expand \left(x-5\right)^{2}.

$$\frac{248+10x^{2}-100x}{x^{2}-10x+25}$$

Expand

$$\frac{2\left(5x^{2}-50x+124\right)}{\left(x-5\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times \frac{\left(x-5\right)^{2}}{\left(x-5\right)^{2}}.

$$\frac{-2}{\left(x-5\right)^{2}}+\frac{10\left(x-5\right)^{2}}{\left(x-5\right)^{2}}$$

Since \frac{-2}{\left(x-5\right)^{2}} and \frac{10\left(x-5\right)^{2}}{\left(x-5\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{-2+10\left(x-5\right)^{2}}{\left(x-5\right)^{2}}$$

Do the multiplications in -2+10\left(x-5\right)^{2}.

$$\frac{-2+10x^{2}-100x+250}{\left(x-5\right)^{2}}$$

Combine like terms in -2+10x^{2}-100x+250.

$$\frac{248+10x^{2}-100x}{\left(x-5\right)^{2}}$$

Expand \left(x-5\right)^{2}.

$$\frac{248+10x^{2}-100x}{x^{2}-10x+25}$$