Solve -2/x+1+-3/(1+x)^2

$$\frac { - 2 } { x + 1 } + \frac { - 3 } { ( 1 + x ) ^ { 2 } }$$

Evaluate

$$-\frac{2x+5}{\left(x+1\right)^{2}}$$

Short Solution Steps

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

$$\frac{-2\left(x+1\right)}{\left(x+1\right)^{2}}+\frac{-3}{\left(x+1\right)^{2}}$$

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

$$\frac{-2\left(x+1\right)-3}{\left(x+1\right)^{2}}$$

Do the multiplications in -2\left(x+1\right)-3.

$$\frac{-2x-2-3}{\left(x+1\right)^{2}}$$

Combine like terms in -2x-2-3.

$$\frac{-2x-5}{\left(x+1\right)^{2}}$$

Expand \left(x+1\right)^{2}.

$$\frac{-2x-5}{x^{2}+2x+1}$$

Expand

$$-\frac{2x+5}{\left(x+1\right)^{2}}$$

Short Solution Steps

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

$$\frac{-2\left(x+1\right)}{\left(x+1\right)^{2}}+\frac{-3}{\left(x+1\right)^{2}}$$

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

$$\frac{-2\left(x+1\right)-3}{\left(x+1\right)^{2}}$$

Do the multiplications in -2\left(x+1\right)-3.

$$\frac{-2x-2-3}{\left(x+1\right)^{2}}$$

Combine like terms in -2x-2-3.

$$\frac{-2x-5}{\left(x+1\right)^{2}}$$

Expand \left(x+1\right)^{2}.

$$\frac{-2x-5}{x^{2}+2x+1}$$