Solve m^2+8m+16/m^2-m-20/frac{m^2-11m+27{m^2-8m+15}}

$$\frac{ \frac{ { m }^{ 2 } +8m+16 }{ { m }^{ 2 } -m-20 } }{ \frac{ { m }^{ 2 } -11m+27 }{ { m }^{ 2 } -8m+15 } }$$

Evaluate

$$-\frac{\left(m-3\right)\left(m+4\right)}{-m^{2}+11m-27}$$

Short Solution Steps

Divide \frac{m^{2}+8m+16}{m^{2}-m-20} by \frac{m^{2}-11m+27}{m^{2}-8m+15} by multiplying \frac{m^{2}+8m+16}{m^{2}-m-20} by the reciprocal of \frac{m^{2}-11m+27}{m^{2}-8m+15}.

$$\frac{\left(m^{2}+8m+16\right)\left(m^{2}-8m+15\right)}{\left(m^{2}-m-20\right)\left(m^{2}-11m+27\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-5\right)\left(m-3\right)\left(m+4\right)^{2}}{\left(m-5\right)\left(m+4\right)\left(m-\left(-\frac{1}{2}\sqrt{13}+\frac{11}{2}\right)\right)\left(m-\left(\frac{1}{2}\sqrt{13}+\frac{11}{2}\right)\right)}$$

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

$$\frac{\left(m-3\right)\left(m+4\right)}{\left(m-\left(-\frac{1}{2}\sqrt{13}+\frac{11}{2}\right)\right)\left(m-\left(\frac{1}{2}\sqrt{13}+\frac{11}{2}\right)\right)}$$

Expand the expression.

$$\frac{m^{2}+m-12}{m^{2}-11m+27}$$

Expand

$$\frac{m^{2}+m-12}{m^{2}-11m+27}$$

Short Solution Steps

Divide \frac{m^{2}+8m+16}{m^{2}-m-20} by \frac{m^{2}-11m+27}{m^{2}-8m+15} by multiplying \frac{m^{2}+8m+16}{m^{2}-m-20} by the reciprocal of \frac{m^{2}-11m+27}{m^{2}-8m+15}.

$$\frac{\left(m^{2}+8m+16\right)\left(m^{2}-8m+15\right)}{\left(m^{2}-m-20\right)\left(m^{2}-11m+27\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-5\right)\left(m-3\right)\left(m+4\right)^{2}}{\left(m-5\right)\left(m+4\right)\left(m-\left(-\frac{1}{2}\sqrt{13}+\frac{11}{2}\right)\right)\left(m-\left(\frac{1}{2}\sqrt{13}+\frac{11}{2}\right)\right)}$$

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

$$\frac{\left(m-3\right)\left(m+4\right)}{\left(m-\left(-\frac{1}{2}\sqrt{13}+\frac{11}{2}\right)\right)\left(m-\left(\frac{1}{2}\sqrt{13}+\frac{11}{2}\right)\right)}$$

Expand the expression.

$$\frac{m^{2}+m-12}{m^{2}-11m+27}$$