Solve (1+3/a-2)a^2-4/a+1

$$( 1 + \frac { 3 } { a - 2 } ) \frac { a ^ { 2 } - 4 } { a + 1 }$$

Evaluate

$$a+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a-2}{a-2}.

$$\left(\frac{a-2}{a-2}+\frac{3}{a-2}\right)\times \frac{a^{2}-4}{a+1}$$

Since \frac{a-2}{a-2} and \frac{3}{a-2} have the same denominator, add them by adding their numerators.

$$\frac{a-2+3}{a-2}\times \frac{a^{2}-4}{a+1}$$

Combine like terms in a-2+3.

$$\frac{a+1}{a-2}\times \frac{a^{2}-4}{a+1}$$

Multiply \frac{a+1}{a-2} times \frac{a^{2}-4}{a+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a+1\right)\left(a^{2}-4\right)}{\left(a-2\right)\left(a+1\right)}$$

Cancel out a+1 in both numerator and denominator.

$$\frac{a^{2}-4}{a-2}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-2\right)\left(a+2\right)}{a-2}$$

Cancel out a-2 in both numerator and denominator.

$$a+2$$

Expand

$$a+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a-2}{a-2}.

$$\left(\frac{a-2}{a-2}+\frac{3}{a-2}\right)\times \frac{a^{2}-4}{a+1}$$

Since \frac{a-2}{a-2} and \frac{3}{a-2} have the same denominator, add them by adding their numerators.

$$\frac{a-2+3}{a-2}\times \frac{a^{2}-4}{a+1}$$

Combine like terms in a-2+3.

$$\frac{a+1}{a-2}\times \frac{a^{2}-4}{a+1}$$

Multiply \frac{a+1}{a-2} times \frac{a^{2}-4}{a+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a+1\right)\left(a^{2}-4\right)}{\left(a-2\right)\left(a+1\right)}$$

Cancel out a+1 in both numerator and denominator.

$$\frac{a^{2}-4}{a-2}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-2\right)\left(a+2\right)}{a-2}$$

Cancel out a-2 in both numerator and denominator.

$$a+2$$