Solve 3/a^2-3/a/frac{3{a^2}+3/a}

$$\frac { \frac { 3 } { a ^ { 2 } } - \frac { 3 } { a } } { \frac { 3 } { a ^ { 2 } } + \frac { 3 } { a } }$$

Evaluate

$$-\frac{a-1}{a+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a^{2} and a is a^{2}. Multiply \frac{3}{a} times \frac{a}{a}.

$$\frac{\frac{3}{a^{2}}-\frac{3a}{a^{2}}}{\frac{3}{a^{2}}+\frac{3}{a}}$$

Since \frac{3}{a^{2}} and \frac{3a}{a^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-3a}{a^{2}}}{\frac{3}{a^{2}}+\frac{3}{a}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a^{2} and a is a^{2}. Multiply \frac{3}{a} times \frac{a}{a}.

$$\frac{\frac{3-3a}{a^{2}}}{\frac{3}{a^{2}}+\frac{3a}{a^{2}}}$$

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

$$\frac{\frac{3-3a}{a^{2}}}{\frac{3+3a}{a^{2}}}$$

Divide \frac{3-3a}{a^{2}} by \frac{3+3a}{a^{2}} by multiplying \frac{3-3a}{a^{2}} by the reciprocal of \frac{3+3a}{a^{2}}.

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

Cancel out a^{2} in both numerator and denominator.

$$\frac{-3a+3}{3a+3}$$

Factor the expressions that are not already factored.

$$\frac{3\left(-a+1\right)}{3\left(a+1\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-a+1}{a+1}$$

Expand

$$-\frac{a-1}{a+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a^{2} and a is a^{2}. Multiply \frac{3}{a} times \frac{a}{a}.

$$\frac{\frac{3}{a^{2}}-\frac{3a}{a^{2}}}{\frac{3}{a^{2}}+\frac{3}{a}}$$

Since \frac{3}{a^{2}} and \frac{3a}{a^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-3a}{a^{2}}}{\frac{3}{a^{2}}+\frac{3}{a}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a^{2} and a is a^{2}. Multiply \frac{3}{a} times \frac{a}{a}.

$$\frac{\frac{3-3a}{a^{2}}}{\frac{3}{a^{2}}+\frac{3a}{a^{2}}}$$

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

$$\frac{\frac{3-3a}{a^{2}}}{\frac{3+3a}{a^{2}}}$$

Divide \frac{3-3a}{a^{2}} by \frac{3+3a}{a^{2}} by multiplying \frac{3-3a}{a^{2}} by the reciprocal of \frac{3+3a}{a^{2}}.

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

Cancel out a^{2} in both numerator and denominator.

$$\frac{-3a+3}{3a+3}$$

Factor the expressions that are not already factored.

$$\frac{3\left(-a+1\right)}{3\left(a+1\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-a+1}{a+1}$$