Solve 4/r+1+3/2x+2=

$$\frac { 4 } { r + 1 } + \frac { 3 } { 2 x + 2 } =$$

Evaluate

$$\frac{8x+3r+11}{2\left(r+1\right)\left(x+1\right)}$$

Short Solution Steps

Factor 2x+2.

$$\frac{4}{r+1}+\frac{3}{2\left(x+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of r+1 and 2\left(x+1\right) is 2\left(r+1\right)\left(x+1\right). Multiply \frac{4}{r+1} times \frac{2\left(x+1\right)}{2\left(x+1\right)}. Multiply \frac{3}{2\left(x+1\right)} times \frac{r+1}{r+1}.

$$\frac{4\times 2\left(x+1\right)}{2\left(r+1\right)\left(x+1\right)}+\frac{3\left(r+1\right)}{2\left(r+1\right)\left(x+1\right)}$$

Since \frac{4\times 2\left(x+1\right)}{2\left(r+1\right)\left(x+1\right)} and \frac{3\left(r+1\right)}{2\left(r+1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{4\times 2\left(x+1\right)+3\left(r+1\right)}{2\left(r+1\right)\left(x+1\right)}$$

Do the multiplications in 4\times 2\left(x+1\right)+3\left(r+1\right).

$$\frac{8x+8+3r+3}{2\left(r+1\right)\left(x+1\right)}$$

Combine like terms in 8x+8+3r+3.

$$\frac{8x+11+3r}{2\left(r+1\right)\left(x+1\right)}$$

Expand 2\left(r+1\right)\left(x+1\right).

$$\frac{8x+11+3r}{2rx+2x+2r+2}$$

Factor

$$\frac{8x+3r+11}{2\left(r+1\right)\left(x+1\right)}$$