Solve 5a+5b/2x-2ydiv20b+20a/3y-3x

$$\frac { 5 a + 5 b } { 2 x - 2 y } \div \frac { 20 b + 20 a } { 3 y - 3 x }$$

Evaluate

$$-\frac{3}{8}=-0.375$$

Short Solution Steps

Divide \frac{5a+5b}{2x-2y} by \frac{20b+20a}{3y-3x} by multiplying \frac{5a+5b}{2x-2y} by the reciprocal of \frac{20b+20a}{3y-3x}.

$$\frac{\left(5a+5b\right)\left(3y-3x\right)}{\left(2x-2y\right)\left(20b+20a\right)}$$

Factor the expressions that are not already factored.

$$\frac{3\times 5\left(a+b\right)\left(-x+y\right)}{2\times 20\left(a+b\right)\left(x-y\right)}$$

Extract the negative sign in y-x.

$$\frac{-3\times 5\left(a+b\right)\left(x-y\right)}{2\times 20\left(a+b\right)\left(x-y\right)}$$

Cancel out 5\left(a+b\right)\left(x-y\right) in both numerator and denominator.

$$\frac{-3}{2\times 4}$$

Cancel out -1 in both numerator and denominator.

$$\frac{3}{-2\times 4}$$

Multiply -2 and 4 to get -8.

$$\frac{3}{-8}$$

Fraction \frac{3}{-8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$-\frac{3}{8}$$

Factor

$$-\frac{3}{8} = -0.375$$