Solve x^2-36/2x+10+3/6-x

$$\frac { x ^ { 2 } - 36 } { 2 x + 10 } + \frac { 3 } { 6 - x }$$

Evaluate

$$\frac{-x^{3}+6x^{2}+42x-186}{2\left(6-x\right)\left(x+5\right)}$$

Short Solution Steps

Factor 2x+10.

$$\frac{x^{2}-36}{2\left(x+5\right)}+\frac{3}{6-x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+5\right) and 6-x is 2\left(x+5\right)\left(-x+6\right). Multiply \frac{x^{2}-36}{2\left(x+5\right)} times \frac{-x+6}{-x+6}. Multiply \frac{3}{6-x} times \frac{2\left(x+5\right)}{2\left(x+5\right)}.

$$\frac{\left(x^{2}-36\right)\left(-x+6\right)}{2\left(x+5\right)\left(-x+6\right)}+\frac{3\times 2\left(x+5\right)}{2\left(x+5\right)\left(-x+6\right)}$$

Since \frac{\left(x^{2}-36\right)\left(-x+6\right)}{2\left(x+5\right)\left(-x+6\right)} and \frac{3\times 2\left(x+5\right)}{2\left(x+5\right)\left(-x+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}-36\right)\left(-x+6\right)+3\times 2\left(x+5\right)}{2\left(x+5\right)\left(-x+6\right)}$$

Do the multiplications in \left(x^{2}-36\right)\left(-x+6\right)+3\times 2\left(x+5\right).

$$\frac{-x^{3}+6x^{2}+36x-216+6x+30}{2\left(x+5\right)\left(-x+6\right)}$$

Combine like terms in -x^{3}+6x^{2}+36x-216+6x+30.

$$\frac{-x^{3}+6x^{2}+42x-186}{2\left(x+5\right)\left(-x+6\right)}$$

Expand 2\left(x+5\right)\left(-x+6\right).

$$\frac{-x^{3}+6x^{2}+42x-186}{-2x^{2}+2x+60}$$

Expand

$$-\frac{x^{3}-6x^{2}-42x+186}{2\left(6-x\right)\left(x+5\right)}$$

Short Solution Steps

Factor 2x+10.

$$\frac{x^{2}-36}{2\left(x+5\right)}+\frac{3}{6-x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+5\right) and 6-x is 2\left(x+5\right)\left(-x+6\right). Multiply \frac{x^{2}-36}{2\left(x+5\right)} times \frac{-x+6}{-x+6}. Multiply \frac{3}{6-x} times \frac{2\left(x+5\right)}{2\left(x+5\right)}.

$$\frac{\left(x^{2}-36\right)\left(-x+6\right)}{2\left(x+5\right)\left(-x+6\right)}+\frac{3\times 2\left(x+5\right)}{2\left(x+5\right)\left(-x+6\right)}$$

Since \frac{\left(x^{2}-36\right)\left(-x+6\right)}{2\left(x+5\right)\left(-x+6\right)} and \frac{3\times 2\left(x+5\right)}{2\left(x+5\right)\left(-x+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}-36\right)\left(-x+6\right)+3\times 2\left(x+5\right)}{2\left(x+5\right)\left(-x+6\right)}$$

Do the multiplications in \left(x^{2}-36\right)\left(-x+6\right)+3\times 2\left(x+5\right).

$$\frac{-x^{3}+6x^{2}+36x-216+6x+30}{2\left(x+5\right)\left(-x+6\right)}$$

Combine like terms in -x^{3}+6x^{2}+36x-216+6x+30.

$$\frac{-x^{3}+6x^{2}+42x-186}{2\left(x+5\right)\left(-x+6\right)}$$

Expand 2\left(x+5\right)\left(-x+6\right).

$$\frac{-x^{3}+6x^{2}+42x-186}{-2x^{2}+2x+60}$$