Solve x^2/36+12x+x^2-x/6+x

$$\frac { x ^ { 2 } } { 36 + 12 x + x ^ { 2 } } - \frac { x } { 6 + x }$$

Evaluate

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

Short Solution Steps

Factor 36+12x+x^{2}.

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

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

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

Since \frac{x^{2}}{\left(x+6\right)^{2}} and \frac{x\left(x+6\right)}{\left(x+6\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Combine like terms in x^{2}-x^{2}-6x.

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

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

$$\frac{-6x}{x^{2}+12x+36}$$

Factor

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