Solve 2k^2+k-1/1-3k-4k^2div2k^2-k/1-16k^2

$$\frac { 2 k ^ { 2 } + k - 1 } { 1 - 3 k - 4 k ^ { 2 } } \div \frac { 2 k ^ { 2 } - k } { 1 - 16 k ^ { 2 } }$$

Evaluate

$$4+\frac{1}{k}$$

Short Solution Steps

Divide \frac{2k^{2}+k-1}{1-3k-4k^{2}} by \frac{2k^{2}-k}{1-16k^{2}} by multiplying \frac{2k^{2}+k-1}{1-3k-4k^{2}} by the reciprocal of \frac{2k^{2}-k}{1-16k^{2}}.

$$\frac{\left(2k^{2}+k-1\right)\left(1-16k^{2}\right)}{\left(1-3k-4k^{2}\right)\left(2k^{2}-k\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 1+k.

$$\frac{-\left(-4k-1\right)\left(-k-1\right)\left(2k-1\right)\left(4k-1\right)}{k\left(-k-1\right)\left(2k-1\right)\left(4k-1\right)}$$

Cancel out \left(-k-1\right)\left(2k-1\right)\left(4k-1\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{4k+1}{k}$$

Expand

$$4+\frac{1}{k}$$

Short Solution Steps

Divide \frac{2k^{2}+k-1}{1-3k-4k^{2}} by \frac{2k^{2}-k}{1-16k^{2}} by multiplying \frac{2k^{2}+k-1}{1-3k-4k^{2}} by the reciprocal of \frac{2k^{2}-k}{1-16k^{2}}.

$$\frac{\left(2k^{2}+k-1\right)\left(1-16k^{2}\right)}{\left(1-3k-4k^{2}\right)\left(2k^{2}-k\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 1+k.

$$\frac{-\left(-4k-1\right)\left(-k-1\right)\left(2k-1\right)\left(4k-1\right)}{k\left(-k-1\right)\left(2k-1\right)\left(4k-1\right)}$$

Cancel out \left(-k-1\right)\left(2k-1\right)\left(4k-1\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{4k+1}{k}$$