Solve +(3c^2+2m^2)[1/m+n]+13

$$+ ( 3 c ^ { 2 } + 2 m ^ { 2 } ) [ \frac { 1 } { m + n } ] + 13$$

Evaluate

$$\frac{2m^{2}+13m+13n+3c^{2}}{m+n}$$

Short Solution Steps

Express \left(3c^{2}+2m^{2}\right)\times \frac{1}{m+n} as a single fraction.

$$\frac{3c^{2}+2m^{2}}{m+n}+13$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 13 times \frac{m+n}{m+n}.

$$\frac{3c^{2}+2m^{2}}{m+n}+\frac{13\left(m+n\right)}{m+n}$$

Since \frac{3c^{2}+2m^{2}}{m+n} and \frac{13\left(m+n\right)}{m+n} have the same denominator, add them by adding their numerators.

$$\frac{3c^{2}+2m^{2}+13\left(m+n\right)}{m+n}$$

Do the multiplications in 3c^{2}+2m^{2}+13\left(m+n\right).

$$\frac{3c^{2}+2m^{2}+13m+13n}{m+n}$$

Expand

$$\frac{2m^{2}+13m+13n+3c^{2}}{m+n}$$

Short Solution Steps

Express \left(3c^{2}+2m^{2}\right)\times \frac{1}{m+n} as a single fraction.

$$\frac{3c^{2}+2m^{2}}{m+n}+13$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 13 times \frac{m+n}{m+n}.

$$\frac{3c^{2}+2m^{2}}{m+n}+\frac{13\left(m+n\right)}{m+n}$$

Since \frac{3c^{2}+2m^{2}}{m+n} and \frac{13\left(m+n\right)}{m+n} have the same denominator, add them by adding their numerators.

$$\frac{3c^{2}+2m^{2}+13\left(m+n\right)}{m+n}$$

Do the multiplications in 3c^{2}+2m^{2}+13\left(m+n\right).

$$\frac{3c^{2}+2m^{2}+13m+13n}{m+n}$$