Solve 8k+k^2+16/15k^2+3k:16-k^2/25k^2-1

$$\frac { 8 k + k ^ { 2 } + 16 } { 15 k ^ { 2 } + 3 k } : \frac { 16 - k ^ { 2 } } { 25 k ^ { 2 } - 1 }$$

Evaluate

$$-\frac{\left(5k-1\right)\left(k+4\right)}{3k\left(k-4\right)}$$

Short Solution Steps

Divide \frac{8k+k^{2}+16}{15k^{2}+3k} by \frac{16-k^{2}}{25k^{2}-1} by multiplying \frac{8k+k^{2}+16}{15k^{2}+3k} by the reciprocal of \frac{16-k^{2}}{25k^{2}-1}.

$$\frac{\left(8k+k^{2}+16\right)\left(25k^{2}-1\right)}{\left(15k^{2}+3k\right)\left(16-k^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(5k-1\right)\left(5k+1\right)\left(k+4\right)^{2}}{3k\left(k-4\right)\left(-k-4\right)\left(5k+1\right)}$$

Cancel out 5k+1 in both numerator and denominator.

$$\frac{\left(5k-1\right)\left(k+4\right)^{2}}{3k\left(k-4\right)\left(-k-4\right)}$$

Expand the expression.

$$\frac{5k^{3}+39k^{2}+72k-16}{-3k^{3}+48k}$$

Expand

$$\frac{5k^{2}+19k-4}{3k\left(4-k\right)}$$

Short Solution Steps

Divide \frac{8k+k^{2}+16}{15k^{2}+3k} by \frac{16-k^{2}}{25k^{2}-1} by multiplying \frac{8k+k^{2}+16}{15k^{2}+3k} by the reciprocal of \frac{16-k^{2}}{25k^{2}-1}.

$$\frac{\left(8k+k^{2}+16\right)\left(25k^{2}-1\right)}{\left(15k^{2}+3k\right)\left(16-k^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(5k-1\right)\left(5k+1\right)\left(k+4\right)^{2}}{3k\left(k-4\right)\left(-k-4\right)\left(5k+1\right)}$$

Cancel out 5k+1 in both numerator and denominator.

$$\frac{\left(5k-1\right)\left(k+4\right)^{2}}{3k\left(k-4\right)\left(-k-4\right)}$$

Expand the expression.

$$\frac{5k^{3}+39k^{2}+72k-16}{-3k^{3}+48k}$$