Solve -30+50/(x+6)^2

$$- 30 + \frac { 50 } { ( x + 6 ) ^ { 2 } }$$

Evaluate

$$-\frac{10\left(3x^{2}+36x+103\right)}{\left(x+6\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -30 times \frac{\left(x+6\right)^{2}}{\left(x+6\right)^{2}}.

$$-\frac{30\left(x+6\right)^{2}}{\left(x+6\right)^{2}}+\frac{50}{\left(x+6\right)^{2}}$$

Since -\frac{30\left(x+6\right)^{2}}{\left(x+6\right)^{2}} and \frac{50}{\left(x+6\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{-30\left(x+6\right)^{2}+50}{\left(x+6\right)^{2}}$$

Do the multiplications in -30\left(x+6\right)^{2}+50.

$$\frac{-30x^{2}-360x-1080+50}{\left(x+6\right)^{2}}$$

Combine like terms in -30x^{2}-360x-1080+50.

$$\frac{-30x^{2}-360x-1030}{\left(x+6\right)^{2}}$$

Expand \left(x+6\right)^{2}.

$$\frac{-30x^{2}-360x-1030}{x^{2}+12x+36}$$

Expand

$$-\frac{10\left(3x^{2}+36x+103\right)}{\left(x+6\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -30 times \frac{\left(x+6\right)^{2}}{\left(x+6\right)^{2}}.

$$-\frac{30\left(x+6\right)^{2}}{\left(x+6\right)^{2}}+\frac{50}{\left(x+6\right)^{2}}$$

Since -\frac{30\left(x+6\right)^{2}}{\left(x+6\right)^{2}} and \frac{50}{\left(x+6\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{-30\left(x+6\right)^{2}+50}{\left(x+6\right)^{2}}$$

Do the multiplications in -30\left(x+6\right)^{2}+50.

$$\frac{-30x^{2}-360x-1080+50}{\left(x+6\right)^{2}}$$

Combine like terms in -30x^{2}-360x-1080+50.

$$\frac{-30x^{2}-360x-1030}{\left(x+6\right)^{2}}$$

Expand \left(x+6\right)^{2}.

$$\frac{-30x^{2}-360x-1030}{x^{2}+12x+36}$$