Solve m/m^2+5m-7/5+m-n-5/4m+20=

$$\frac { m } { m ^ { 2 } + 5 m } - \frac { 7 } { 5 + m } - \frac { n - 5 } { 4 m + 20 } =$$

Evaluate

$$-\frac{n+19}{4\left(m+5\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m}{m^{2}+5m}.

$$\frac{m}{m\left(m+5\right)}-\frac{7}{5+m}-\frac{n-5}{4m+20}$$

Cancel out m in both numerator and denominator.

$$\frac{1}{m+5}-\frac{7}{5+m}-\frac{n-5}{4m+20}$$

Since \frac{1}{m+5} and \frac{7}{5+m} have the same denominator, subtract them by subtracting their numerators. Subtract 7 from 1 to get -6.

$$\frac{-6}{m+5}-\frac{n-5}{4m+20}$$

Factor 4m+20.

$$\frac{-6}{m+5}-\frac{n-5}{4\left(m+5\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m+5 and 4\left(m+5\right) is 4\left(m+5\right). Multiply \frac{-6}{m+5} times \frac{4}{4}.

$$\frac{-6\times 4}{4\left(m+5\right)}-\frac{n-5}{4\left(m+5\right)}$$

Since \frac{-6\times 4}{4\left(m+5\right)} and \frac{n-5}{4\left(m+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-6\times 4-\left(n-5\right)}{4\left(m+5\right)}$$

Do the multiplications in -6\times 4-\left(n-5\right).

$$\frac{-24-n+5}{4\left(m+5\right)}$$

Combine like terms in -24-n+5.

$$\frac{-19-n}{4\left(m+5\right)}$$

Expand 4\left(m+5\right).

$$\frac{-19-n}{4m+20}$$

Expand

$$-\frac{n+19}{4\left(m+5\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{m}{m^{2}+5m}.

$$\frac{m}{m\left(m+5\right)}-\frac{7}{5+m}-\frac{n-5}{4m+20}$$

Cancel out m in both numerator and denominator.

$$\frac{1}{m+5}-\frac{7}{5+m}-\frac{n-5}{4m+20}$$

Since \frac{1}{m+5} and \frac{7}{5+m} have the same denominator, subtract them by subtracting their numerators. Subtract 7 from 1 to get -6.

$$\frac{-6}{m+5}-\frac{n-5}{4m+20}$$

Factor 4m+20.

$$\frac{-6}{m+5}-\frac{n-5}{4\left(m+5\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m+5 and 4\left(m+5\right) is 4\left(m+5\right). Multiply \frac{-6}{m+5} times \frac{4}{4}.

$$\frac{-6\times 4}{4\left(m+5\right)}-\frac{n-5}{4\left(m+5\right)}$$

Since \frac{-6\times 4}{4\left(m+5\right)} and \frac{n-5}{4\left(m+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-6\times 4-\left(n-5\right)}{4\left(m+5\right)}$$

Do the multiplications in -6\times 4-\left(n-5\right).

$$\frac{-24-n+5}{4\left(m+5\right)}$$

Combine like terms in -24-n+5.

$$\frac{-19-n}{4\left(m+5\right)}$$

Expand 4\left(m+5\right).

$$\frac{-19-n}{4m+20}$$