Solve n^2+8n+16/n^2-n-20divn^2-11m+24/n^2-8n+15

$$\frac { n ^ { 2 } + 8 n + 16 } { n ^ { 2 } - n - 20 } \div \frac { n ^ { 2 } - 11 m + 24 } { n ^ { 2 } - 8 n + 15 }$$

Evaluate

$$\frac{\left(n-3\right)\left(n+4\right)}{24+n^{2}-11m}$$

Short Solution Steps

Divide \frac{n^{2}+8n+16}{n^{2}-n-20} by \frac{n^{2}-11m+24}{n^{2}-8n+15} by multiplying \frac{n^{2}+8n+16}{n^{2}-n-20} by the reciprocal of \frac{n^{2}-11m+24}{n^{2}-8n+15}.

$$\frac{\left(n^{2}+8n+16\right)\left(n^{2}-8n+15\right)}{\left(n^{2}-n-20\right)\left(n^{2}-11m+24\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(n-5\right)\left(n-3\right)\left(n+4\right)^{2}}{\left(n-5\right)\left(n+4\right)\left(-11m+n^{2}+24\right)}$$

Cancel out \left(n-5\right)\left(n+4\right) in both numerator and denominator.

$$\frac{\left(n-3\right)\left(n+4\right)}{-11m+n^{2}+24}$$

Expand the expression.

$$\frac{n^{2}+n-12}{-11m+n^{2}+24}$$

Expand

$$\frac{n^{2}+n-12}{24+n^{2}-11m}$$

Short Solution Steps

Divide \frac{n^{2}+8n+16}{n^{2}-n-20} by \frac{n^{2}-11m+24}{n^{2}-8n+15} by multiplying \frac{n^{2}+8n+16}{n^{2}-n-20} by the reciprocal of \frac{n^{2}-11m+24}{n^{2}-8n+15}.

$$\frac{\left(n^{2}+8n+16\right)\left(n^{2}-8n+15\right)}{\left(n^{2}-n-20\right)\left(n^{2}-11m+24\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(n-5\right)\left(n-3\right)\left(n+4\right)^{2}}{\left(n-5\right)\left(n+4\right)\left(-11m+n^{2}+24\right)}$$

Cancel out \left(n-5\right)\left(n+4\right) in both numerator and denominator.

$$\frac{\left(n-3\right)\left(n+4\right)}{-11m+n^{2}+24}$$

Expand the expression.

$$\frac{n^{2}+n-12}{-11m+n^{2}+24}$$