Solve k(-4+16k^2/1+4k^2-4)

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

Evaluate

$$-\frac{8k}{4k^{2}+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{1+4k^{2}}{1+4k^{2}}.

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

Since \frac{-4+16k^{2}}{1+4k^{2}} and \frac{4\left(1+4k^{2}\right)}{1+4k^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -4+16k^{2}-4\left(1+4k^{2}\right).

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

Combine like terms in -4+16k^{2}-4-16k^{2}.

$$k\times \frac{-8}{1+4k^{2}}$$

Express k\times \frac{-8}{1+4k^{2}} as a single fraction.

$$\frac{k\left(-8\right)}{1+4k^{2}}$$

Expand

$$-\frac{8k}{4k^{2}+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{1+4k^{2}}{1+4k^{2}}.

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

Since \frac{-4+16k^{2}}{1+4k^{2}} and \frac{4\left(1+4k^{2}\right)}{1+4k^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -4+16k^{2}-4\left(1+4k^{2}\right).

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

Combine like terms in -4+16k^{2}-4-16k^{2}.

$$k\times \frac{-8}{1+4k^{2}}$$

Express k\times \frac{-8}{1+4k^{2}} as a single fraction.

$$\frac{k\left(-8\right)}{1+4k^{2}}$$