Solve -5/b-5-3/frac{10{b-5}+6}

$$\frac { \frac { - 5 } { b - 5 } - 3 } { \frac { 10 } { b - 5 } + 6 }$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{b-5}{b-5}.

$$\frac{\frac{-5}{b-5}-\frac{3\left(b-5\right)}{b-5}}{\frac{10}{b-5}+6}$$

Since \frac{-5}{b-5} and \frac{3\left(b-5\right)}{b-5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-5-3\left(b-5\right)}{b-5}}{\frac{10}{b-5}+6}$$

Do the multiplications in -5-3\left(b-5\right).

$$\frac{\frac{-5-3b+15}{b-5}}{\frac{10}{b-5}+6}$$

Combine like terms in -5-3b+15.

$$\frac{\frac{10-3b}{b-5}}{\frac{10}{b-5}+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{b-5}{b-5}.

$$\frac{\frac{10-3b}{b-5}}{\frac{10}{b-5}+\frac{6\left(b-5\right)}{b-5}}$$

Since \frac{10}{b-5} and \frac{6\left(b-5\right)}{b-5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10-3b}{b-5}}{\frac{10+6\left(b-5\right)}{b-5}}$$

Do the multiplications in 10+6\left(b-5\right).

$$\frac{\frac{10-3b}{b-5}}{\frac{10+6b-30}{b-5}}$$

Combine like terms in 10+6b-30.

$$\frac{\frac{10-3b}{b-5}}{\frac{-20+6b}{b-5}}$$

Divide \frac{10-3b}{b-5} by \frac{-20+6b}{b-5} by multiplying \frac{10-3b}{b-5} by the reciprocal of \frac{-20+6b}{b-5}.

$$\frac{\left(10-3b\right)\left(b-5\right)}{\left(b-5\right)\left(-20+6b\right)}$$

Cancel out b-5 in both numerator and denominator.

$$\frac{-3b+10}{6b-20}$$

Factor the expressions that are not already factored.

$$\frac{-3b+10}{2\left(3b-10\right)}$$

Extract the negative sign in 10-3b.

$$\frac{-\left(3b-10\right)}{2\left(3b-10\right)}$$

Cancel out 3b-10 in both numerator and denominator.

$$\frac{-1}{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$-\frac{1}{2}$$

Factor

$$-\frac{1}{2} = -0.5$$