Solve x^2/a-x/frac{a^2+2ax-x^2{a}}

$$\frac { \frac { x ^ { 2 } } { a } - x } { \frac { a ^ { 2 } + 2 a x - x ^ { 2 } } { a } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{a}{a}.

$$\frac{\frac{x^{2}}{a}-\frac{xa}{a}}{\frac{a^{2}+2ax-x^{2}}{a}}$$

Since \frac{x^{2}}{a} and \frac{xa}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-xa}{a}}{\frac{a^{2}+2ax-x^{2}}{a}}$$

Divide \frac{x^{2}-xa}{a} by \frac{a^{2}+2ax-x^{2}}{a} by multiplying \frac{x^{2}-xa}{a} by the reciprocal of \frac{a^{2}+2ax-x^{2}}{a}.

$$\frac{\left(x^{2}-xa\right)a}{a\left(a^{2}+2ax-x^{2}\right)}$$

Cancel out a in both numerator and denominator.

$$\frac{x^{2}-ax}{-x^{2}+2ax+a^{2}}$$

Expand

$$\frac{x^{2}-ax}{a^{2}+2ax-x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{a}{a}.

$$\frac{\frac{x^{2}}{a}-\frac{xa}{a}}{\frac{a^{2}+2ax-x^{2}}{a}}$$

Since \frac{x^{2}}{a} and \frac{xa}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-xa}{a}}{\frac{a^{2}+2ax-x^{2}}{a}}$$

Divide \frac{x^{2}-xa}{a} by \frac{a^{2}+2ax-x^{2}}{a} by multiplying \frac{x^{2}-xa}{a} by the reciprocal of \frac{a^{2}+2ax-x^{2}}{a}.

$$\frac{\left(x^{2}-xa\right)a}{a\left(a^{2}+2ax-x^{2}\right)}$$

Cancel out a in both numerator and denominator.

$$\frac{x^{2}-ax}{-x^{2}+2ax+a^{2}}$$