Solve 5/4h+4+3/h^2+h

$$\frac { 5 } { 4 h + 4 } + \frac { 3 } { h ^ { 2 } + h }$$

Evaluate

$$\frac{5h+12}{4h\left(h+1\right)}$$

Short Solution Steps

Factor 4h+4. Factor h^{2}+h.

$$\frac{5}{4\left(h+1\right)}+\frac{3}{h\left(h+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(h+1\right) and h\left(h+1\right) is 4h\left(h+1\right). Multiply \frac{5}{4\left(h+1\right)} times \frac{h}{h}. Multiply \frac{3}{h\left(h+1\right)} times \frac{4}{4}.

$$\frac{5h}{4h\left(h+1\right)}+\frac{3\times 4}{4h\left(h+1\right)}$$

Since \frac{5h}{4h\left(h+1\right)} and \frac{3\times 4}{4h\left(h+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{5h+3\times 4}{4h\left(h+1\right)}$$

Do the multiplications in 5h+3\times 4.

$$\frac{5h+12}{4h\left(h+1\right)}$$

Expand 4h\left(h+1\right).

$$\frac{5h+12}{4h^{2}+4h}$$

Factor

$$\frac{5h+12}{4h\left(h+1\right)}$$