Solve a^2-b^2/c^2-d^2:b-a/c+d

$$\frac { a ^ { 2 } - b ^ { 2 } } { c ^ { 2 } - d ^ { 2 } } : \frac { b - a } { c + d }$$

Evaluate

$$-\frac{a+b}{c-d}$$

Short Solution Steps

Divide \frac{a^{2}-b^{2}}{c^{2}-d^{2}} by \frac{b-a}{c+d} by multiplying \frac{a^{2}-b^{2}}{c^{2}-d^{2}} by the reciprocal of \frac{b-a}{c+d}.

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

Factor the expressions that are not already factored.

$$\frac{\left(a+b\right)\left(a-b\right)\left(c+d\right)}{\left(-a+b\right)\left(c+d\right)\left(c-d\right)}$$

Extract the negative sign in a-b.

$$\frac{-\left(a+b\right)\left(-a+b\right)\left(c+d\right)}{\left(-a+b\right)\left(c+d\right)\left(c-d\right)}$$

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

$$\frac{-\left(a+b\right)}{c-d}$$

Expand the expression.

$$\frac{-a-b}{c-d}$$

Expand

$$-\frac{a+b}{c-d}$$

Short Solution Steps

Divide \frac{a^{2}-b^{2}}{c^{2}-d^{2}} by \frac{b-a}{c+d} by multiplying \frac{a^{2}-b^{2}}{c^{2}-d^{2}} by the reciprocal of \frac{b-a}{c+d}.

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

Factor the expressions that are not already factored.

$$\frac{\left(a+b\right)\left(a-b\right)\left(c+d\right)}{\left(-a+b\right)\left(c+d\right)\left(c-d\right)}$$

Extract the negative sign in a-b.

$$\frac{-\left(a+b\right)\left(-a+b\right)\left(c+d\right)}{\left(-a+b\right)\left(c+d\right)\left(c-d\right)}$$

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

$$\frac{-\left(a+b\right)}{c-d}$$

Expand the expression.

$$\frac{-a-b}{c-d}$$