Solve 3/yv^2+8/y^2v

$$\frac { 3 } { y v ^ { 2 } } + \frac { 8 } { y ^ { 2 } v }$$

Evaluate

$$\frac{3y+8v}{\left(vy\right)^{2}}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of yv^{2} and y^{2}v is v^{2}y^{2}. Multiply \frac{3}{yv^{2}} times \frac{y}{y}. Multiply \frac{8}{y^{2}v} times \frac{v}{v}.

$$\frac{3y}{v^{2}y^{2}}+\frac{8v}{v^{2}y^{2}}$$

Since \frac{3y}{v^{2}y^{2}} and \frac{8v}{v^{2}y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3y+8v}{v^{2}y^{2}}$$

Factor

$$\frac{3y+8v}{\left(vy\right)^{2}}$$