Solve m^2-49/m+1div7-m/m^2-1

$$\frac { m ^ { 2 } - 49 } { m + 1 } \div \frac { 7 - m } { m ^ { 2 } - 1 }$$

Evaluate

$$-\left(m-1\right)\left(m+7\right)$$

Short Solution Steps

Divide \frac{m^{2}-49}{m+1} by \frac{7-m}{m^{2}-1} by multiplying \frac{m^{2}-49}{m+1} by the reciprocal of \frac{7-m}{m^{2}-1}.

$$\frac{\left(m^{2}-49\right)\left(m^{2}-1\right)}{\left(m+1\right)\left(7-m\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-7\right)\left(m-1\right)\left(m+1\right)\left(m+7\right)}{\left(m+1\right)\left(-m+7\right)}$$

Extract the negative sign in -7+m.

$$\frac{-\left(m-1\right)\left(m+1\right)\left(m+7\right)\left(-m+7\right)}{\left(m+1\right)\left(-m+7\right)}$$

Cancel out \left(m+1\right)\left(-m+7\right) in both numerator and denominator.

$$-\left(m-1\right)\left(m+7\right)$$

Expand the expression.

$$-m^{2}-6m+7$$

Expand

$$7-6m-m^{2}$$

Short Solution Steps

Divide \frac{m^{2}-49}{m+1} by \frac{7-m}{m^{2}-1} by multiplying \frac{m^{2}-49}{m+1} by the reciprocal of \frac{7-m}{m^{2}-1}.

$$\frac{\left(m^{2}-49\right)\left(m^{2}-1\right)}{\left(m+1\right)\left(7-m\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-7\right)\left(m-1\right)\left(m+1\right)\left(m+7\right)}{\left(m+1\right)\left(-m+7\right)}$$

Extract the negative sign in -7+m.

$$\frac{-\left(m-1\right)\left(m+1\right)\left(m+7\right)\left(-m+7\right)}{\left(m+1\right)\left(-m+7\right)}$$

Cancel out \left(m+1\right)\left(-m+7\right) in both numerator and denominator.

$$-\left(m-1\right)\left(m+7\right)$$

Expand the expression.

$$-m^{2}-6m+7$$