Solve m/2+8m+15/2m/frac{1{2}+5/2m}

$$\frac { \frac { m } { 2 } + \frac { 8 m + 15 } { 2 m } } { \frac { 1 } { 2 } + \frac { 5 } { 2 m } }$$

Evaluate

$$m+3$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2m is 2m. Multiply \frac{m}{2} times \frac{m}{m}.

$$\frac{\frac{mm}{2m}+\frac{8m+15}{2m}}{\frac{1}{2}+\frac{5}{2m}}$$

Since \frac{mm}{2m} and \frac{8m+15}{2m} have the same denominator, add them by adding their numerators.

$$\frac{\frac{mm+8m+15}{2m}}{\frac{1}{2}+\frac{5}{2m}}$$

Do the multiplications in mm+8m+15.

$$\frac{\frac{m^{2}+8m+15}{2m}}{\frac{1}{2}+\frac{5}{2m}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2m is 2m. Multiply \frac{1}{2} times \frac{m}{m}.

$$\frac{\frac{m^{2}+8m+15}{2m}}{\frac{m}{2m}+\frac{5}{2m}}$$

Since \frac{m}{2m} and \frac{5}{2m} have the same denominator, add them by adding their numerators.

$$\frac{\frac{m^{2}+8m+15}{2m}}{\frac{m+5}{2m}}$$

Divide \frac{m^{2}+8m+15}{2m} by \frac{m+5}{2m} by multiplying \frac{m^{2}+8m+15}{2m} by the reciprocal of \frac{m+5}{2m}.

$$\frac{\left(m^{2}+8m+15\right)\times 2m}{2m\left(m+5\right)}$$

Cancel out 2m in both numerator and denominator.

$$\frac{m^{2}+8m+15}{m+5}$$

Factor the expressions that are not already factored.

$$\frac{\left(m+3\right)\left(m+5\right)}{m+5}$$

Cancel out m+5 in both numerator and denominator.

$$m+3$$

Expand

$$m+3$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2m is 2m. Multiply \frac{m}{2} times \frac{m}{m}.

$$\frac{\frac{mm}{2m}+\frac{8m+15}{2m}}{\frac{1}{2}+\frac{5}{2m}}$$

Since \frac{mm}{2m} and \frac{8m+15}{2m} have the same denominator, add them by adding their numerators.

$$\frac{\frac{mm+8m+15}{2m}}{\frac{1}{2}+\frac{5}{2m}}$$

Do the multiplications in mm+8m+15.

$$\frac{\frac{m^{2}+8m+15}{2m}}{\frac{1}{2}+\frac{5}{2m}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2m is 2m. Multiply \frac{1}{2} times \frac{m}{m}.

$$\frac{\frac{m^{2}+8m+15}{2m}}{\frac{m}{2m}+\frac{5}{2m}}$$

Since \frac{m}{2m} and \frac{5}{2m} have the same denominator, add them by adding their numerators.

$$\frac{\frac{m^{2}+8m+15}{2m}}{\frac{m+5}{2m}}$$

Divide \frac{m^{2}+8m+15}{2m} by \frac{m+5}{2m} by multiplying \frac{m^{2}+8m+15}{2m} by the reciprocal of \frac{m+5}{2m}.

$$\frac{\left(m^{2}+8m+15\right)\times 2m}{2m\left(m+5\right)}$$

Cancel out 2m in both numerator and denominator.

$$\frac{m^{2}+8m+15}{m+5}$$

Factor the expressions that are not already factored.

$$\frac{\left(m+3\right)\left(m+5\right)}{m+5}$$

Cancel out m+5 in both numerator and denominator.

$$m+3$$