Solve 8k^2-8k-2/1+4k^2-8k^2+8k-2/1+4k^2

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

Evaluate

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

Short Solution Steps

Since \frac{8k^{2}-8k-2}{1+4k^{2}} and \frac{8k^{2}+8k-2}{1+4k^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 8k^{2}-8k-2-\left(8k^{2}+8k-2\right).

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

Combine like terms in 8k^{2}-8k-2-8k^{2}-8k+2.

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

Expand

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

Short Solution Steps

Since \frac{8k^{2}-8k-2}{1+4k^{2}} and \frac{8k^{2}+8k-2}{1+4k^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 8k^{2}-8k-2-\left(8k^{2}+8k-2\right).

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

Combine like terms in 8k^{2}-8k-2-8k^{2}-8k+2.

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