Solve M+1/M-6+M+4/M+9

$$\frac { M + 1 } { M - 6 } + \frac { M + 4 } { M + 9 }$$

Evaluate

$$\frac{2M^{2}+8M-15}{\left(M-6\right)\left(M+9\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of M-6 and M+9 is \left(M-6\right)\left(M+9\right). Multiply \frac{M+1}{M-6} times \frac{M+9}{M+9}. Multiply \frac{M+4}{M+9} times \frac{M-6}{M-6}.

$$\frac{\left(M+1\right)\left(M+9\right)}{\left(M-6\right)\left(M+9\right)}+\frac{\left(M+4\right)\left(M-6\right)}{\left(M-6\right)\left(M+9\right)}$$

Since \frac{\left(M+1\right)\left(M+9\right)}{\left(M-6\right)\left(M+9\right)} and \frac{\left(M+4\right)\left(M-6\right)}{\left(M-6\right)\left(M+9\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(M+1\right)\left(M+9\right)+\left(M+4\right)\left(M-6\right)}{\left(M-6\right)\left(M+9\right)}$$

Do the multiplications in \left(M+1\right)\left(M+9\right)+\left(M+4\right)\left(M-6\right).

$$\frac{M^{2}+9M+M+9+M^{2}-6M+4M-24}{\left(M-6\right)\left(M+9\right)}$$

Combine like terms in M^{2}+9M+M+9+M^{2}-6M+4M-24.

$$\frac{2M^{2}+8M-15}{\left(M-6\right)\left(M+9\right)}$$

Expand \left(M-6\right)\left(M+9\right).

$$\frac{2M^{2}+8M-15}{M^{2}+3M-54}$$

Expand

$$\frac{2M^{2}+8M-15}{\left(M-6\right)\left(M+9\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of M-6 and M+9 is \left(M-6\right)\left(M+9\right). Multiply \frac{M+1}{M-6} times \frac{M+9}{M+9}. Multiply \frac{M+4}{M+9} times \frac{M-6}{M-6}.

$$\frac{\left(M+1\right)\left(M+9\right)}{\left(M-6\right)\left(M+9\right)}+\frac{\left(M+4\right)\left(M-6\right)}{\left(M-6\right)\left(M+9\right)}$$

Since \frac{\left(M+1\right)\left(M+9\right)}{\left(M-6\right)\left(M+9\right)} and \frac{\left(M+4\right)\left(M-6\right)}{\left(M-6\right)\left(M+9\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(M+1\right)\left(M+9\right)+\left(M+4\right)\left(M-6\right)}{\left(M-6\right)\left(M+9\right)}$$

Do the multiplications in \left(M+1\right)\left(M+9\right)+\left(M+4\right)\left(M-6\right).

$$\frac{M^{2}+9M+M+9+M^{2}-6M+4M-24}{\left(M-6\right)\left(M+9\right)}$$

Combine like terms in M^{2}+9M+M+9+M^{2}-6M+4M-24.

$$\frac{2M^{2}+8M-15}{\left(M-6\right)\left(M+9\right)}$$

Expand \left(M-6\right)\left(M+9\right).

$$\frac{2M^{2}+8M-15}{M^{2}+3M-54}$$