Solve x+1/x+2:x+1/x-1+4x+11/x+2

$$\frac { x + 1 } { x + 2 } : \frac { x + 1 } { x - 1 } + \frac { 4 x + 11 } { x + 2 }$$

Evaluate

$$5$$

Short Solution Steps

Divide \frac{x+1}{x+2} by \frac{x+1}{x-1} by multiplying \frac{x+1}{x+2} by the reciprocal of \frac{x+1}{x-1}.

$$\frac{\left(x+1\right)\left(x-1\right)}{\left(x+2\right)\left(x+1\right)}+\frac{4x+11}{x+2}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{x-1}{x+2}+\frac{4x+11}{x+2}$$

Since \frac{x-1}{x+2} and \frac{4x+11}{x+2} have the same denominator, add them by adding their numerators.

$$\frac{x-1+4x+11}{x+2}$$

Combine like terms in x-1+4x+11.

$$\frac{5x+10}{x+2}$$

Factor the expressions that are not already factored in \frac{5x+10}{x+2}.

$$\frac{5\left(x+2\right)}{x+2}$$

Cancel out x+2 in both numerator and denominator.

$$5$$

Factor

$$5$$