Solve (a-b)^2/(a+b)(a-b)diva(a-b)/a-2/a+b

$$\frac { ( a - b ) ^ { 2 } } { ( a + b ) ( a - b ) } \div \frac { a ( a - b ) } { a } - \frac { 2 } { a + b }$$

Evaluate

$$-\frac{1}{a+b}$$

Solution Steps

Divide \frac{\left(a-b\right)^{2}}{\left(a+b\right)\left(a-b\right)} by \frac{a\left(a-b\right)}{a} by multiplying \frac{\left(a-b\right)^{2}}{\left(a+b\right)\left(a-b\right)} by the reciprocal of \frac{a\left(a-b\right)}{a}.

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

Cancel out a\left(a-b\right)\left(a-b\right) in both numerator and denominator.

$$\frac{1}{a+b}-\frac{2}{a+b}$$

Since \frac{1}{a+b} and \frac{2}{a+b} have the same denominator, subtract them by subtracting their numerators. Subtract 2 from 1 to get -1.

$$\frac{-1}{a+b}$$

Expand

$$-\frac{1}{a+b}$$

Solution Steps

Divide \frac{\left(a-b\right)^{2}}{\left(a+b\right)\left(a-b\right)} by \frac{a\left(a-b\right)}{a} by multiplying \frac{\left(a-b\right)^{2}}{\left(a+b\right)\left(a-b\right)} by the reciprocal of \frac{a\left(a-b\right)}{a}.

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

Cancel out a\left(a-b\right)\left(a-b\right) in both numerator and denominator.

$$\frac{1}{a+b}-\frac{2}{a+b}$$

Since \frac{1}{a+b} and \frac{2}{a+b} have the same denominator, subtract them by subtracting their numerators. Subtract 2 from 1 to get -1.

$$\frac{-1}{a+b}$$