Solve f(1-5/a+3)diva^2-4a+4/a^2-9

$$f ( 1 - \frac { 5 } { a + 3 } ) \div \frac { a ^ { 2 } - 4 a + 4 } { a ^ { 2 } - 9 }$$

Evaluate

$$\frac{f\left(a-3\right)}{a-2}$$

$$a\neq 2\text{ and }|a|\neq 3$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a+3}{a+3}.

$$\frac{f\left(\frac{a+3}{a+3}-\frac{5}{a+3}\right)}{\frac{a^{2}-4a+4}{a^{2}-9}}$$

Since \frac{a+3}{a+3} and \frac{5}{a+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{f\times \frac{a+3-5}{a+3}}{\frac{a^{2}-4a+4}{a^{2}-9}}$$

Combine like terms in a+3-5.

$$\frac{f\times \frac{a-2}{a+3}}{\frac{a^{2}-4a+4}{a^{2}-9}}$$

Express f\times \frac{a-2}{a+3} as a single fraction.

$$\frac{\frac{f\left(a-2\right)}{a+3}}{\frac{a^{2}-4a+4}{a^{2}-9}}$$

Divide \frac{f\left(a-2\right)}{a+3} by \frac{a^{2}-4a+4}{a^{2}-9} by multiplying \frac{f\left(a-2\right)}{a+3} by the reciprocal of \frac{a^{2}-4a+4}{a^{2}-9}.

$$\frac{f\left(a-2\right)\left(a^{2}-9\right)}{\left(a+3\right)\left(a^{2}-4a+4\right)}$$

Factor the expressions that are not already factored.

$$\frac{f\left(a-3\right)\left(a-2\right)\left(a+3\right)}{\left(a+3\right)\left(a-2\right)^{2}}$$

Cancel out \left(a-2\right)\left(a+3\right) in both numerator and denominator.

$$\frac{f\left(a-3\right)}{a-2}$$

Expand the expression.

$$\frac{af-3f}{a-2}$$

Expand

$$\frac{af-3f}{a-2}$$

$$a\neq 2\text{ and }|a|\neq 3$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a+3}{a+3}.

$$\frac{f\left(\frac{a+3}{a+3}-\frac{5}{a+3}\right)}{\frac{a^{2}-4a+4}{a^{2}-9}}$$

Since \frac{a+3}{a+3} and \frac{5}{a+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{f\times \frac{a+3-5}{a+3}}{\frac{a^{2}-4a+4}{a^{2}-9}}$$

Combine like terms in a+3-5.

$$\frac{f\times \frac{a-2}{a+3}}{\frac{a^{2}-4a+4}{a^{2}-9}}$$

Express f\times \frac{a-2}{a+3} as a single fraction.

$$\frac{\frac{f\left(a-2\right)}{a+3}}{\frac{a^{2}-4a+4}{a^{2}-9}}$$

Divide \frac{f\left(a-2\right)}{a+3} by \frac{a^{2}-4a+4}{a^{2}-9} by multiplying \frac{f\left(a-2\right)}{a+3} by the reciprocal of \frac{a^{2}-4a+4}{a^{2}-9}.

$$\frac{f\left(a-2\right)\left(a^{2}-9\right)}{\left(a+3\right)\left(a^{2}-4a+4\right)}$$

Factor the expressions that are not already factored.

$$\frac{f\left(a-3\right)\left(a-2\right)\left(a+3\right)}{\left(a+3\right)\left(a-2\right)^{2}}$$

Cancel out \left(a-2\right)\left(a+3\right) in both numerator and denominator.

$$\frac{f\left(a-3\right)}{a-2}$$

Expand the expression.

$$\frac{af-3f}{a-2}$$