Solve mplify (a ^ 2 - 9)/(a ^ 2 - 5a + 6) + (a + 3)/(3a - 6) 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac { a ^ { 2 } - 9 } { a ^ { 2 } - 5 a + 6 } + \frac { a + 3 } { 3 a - 6 } \quad 121$$

Evaluate

$\frac{124\left(a+3\right)}{3\left(a-2\right)}$

Short Solution Steps

Factor the expressions that are not already factored in $\frac{a^{2}-9}{a^{2}-5a+6}$.

$$\frac{\left(a-3\right)\left(a+3\right)}{\left(a-3\right)\left(a-2\right)}+\frac{a+3}{3a-6}\times 121$$

Cancel out $a-3$ in both numerator and denominator.

$$\frac{a+3}{a-2}+\frac{a+3}{3a-6}\times 121$$

Express $\frac{a+3}{3a-6}\times 121$ as a single fraction.

$$\frac{a+3}{a-2}+\frac{\left(a+3\right)\times 121}{3a-6}$$

Factor $3a-6$.

$$\frac{a+3}{a-2}+\frac{\left(a+3\right)\times 121}{3\left(a-2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $a-2$ and $3\left(a-2\right)$ is $3\left(a-2\right)$. Multiply $\frac{a+3}{a-2}$ times $\frac{3}{3}$.

$$\frac{3\left(a+3\right)}{3\left(a-2\right)}+\frac{\left(a+3\right)\times 121}{3\left(a-2\right)}$$

Since $\frac{3\left(a+3\right)}{3\left(a-2\right)}$ and $\frac{\left(a+3\right)\times 121}{3\left(a-2\right)}$ have the same denominator, add them by adding their numerators.

$$\frac{3\left(a+3\right)+\left(a+3\right)\times 121}{3\left(a-2\right)}$$

Do the multiplications in $3\left(a+3\right)+\left(a+3\right)\times 121$.

$$\frac{3a+9+121a+363}{3\left(a-2\right)}$$

Combine like terms in $3a+9+121a+363$.

$$\frac{124a+372}{3\left(a-2\right)}$$

Expand $3\left(a-2\right)$.

$$\frac{124a+372}{3a-6}$$

Expand

$\frac{124\left(a+3\right)}{3\left(a-2\right)}$

Short Solution Steps

Factor the expressions that are not already factored in $\frac{a^{2}-9}{a^{2}-5a+6}$.

$$\frac{\left(a-3\right)\left(a+3\right)}{\left(a-3\right)\left(a-2\right)}+\frac{a+3}{3a-6}\times 121$$

Cancel out $a-3$ in both numerator and denominator.

$$\frac{a+3}{a-2}+\frac{a+3}{3a-6}\times 121$$

Express $\frac{a+3}{3a-6}\times 121$ as a single fraction.

$$\frac{a+3}{a-2}+\frac{\left(a+3\right)\times 121}{3a-6}$$

Factor $3a-6$.

$$\frac{a+3}{a-2}+\frac{\left(a+3\right)\times 121}{3\left(a-2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $a-2$ and $3\left(a-2\right)$ is $3\left(a-2\right)$. Multiply $\frac{a+3}{a-2}$ times $\frac{3}{3}$.

$$\frac{3\left(a+3\right)}{3\left(a-2\right)}+\frac{\left(a+3\right)\times 121}{3\left(a-2\right)}$$

Since $\frac{3\left(a+3\right)}{3\left(a-2\right)}$ and $\frac{\left(a+3\right)\times 121}{3\left(a-2\right)}$ have the same denominator, add them by adding their numerators.

$$\frac{3\left(a+3\right)+\left(a+3\right)\times 121}{3\left(a-2\right)}$$

Do the multiplications in $3\left(a+3\right)+\left(a+3\right)\times 121$.

$$\frac{3a+9+121a+363}{3\left(a-2\right)}$$

Combine like terms in $3a+9+121a+363$.

$$\frac{124a+372}{3\left(a-2\right)}$$

Expand $3\left(a-2\right)$.

$$\frac{124a+372}{3a-6}$$