Solve 8k^2/3+4k^2-44k^2-12/3+4k^2

$$\frac { 8 k ^ { 2 } } { 3 + 4 k ^ { 2 } } - 4 \frac { 4 k ^ { 2 } - 12 } { 3 + 4 k ^ { 2 } }$$

Evaluate

$$\frac{8\left(6-k^{2}\right)}{4k^{2}+3}$$

Short Solution Steps

Express 4\times \frac{4k^{2}-12}{3+4k^{2}} as a single fraction.

$$\frac{8k^{2}}{3+4k^{2}}-\frac{4\left(4k^{2}-12\right)}{3+4k^{2}}$$

Use the distributive property to multiply 4 by 4k^{2}-12.

$$\frac{8k^{2}}{3+4k^{2}}-\frac{16k^{2}-48}{3+4k^{2}}$$

Since \frac{8k^{2}}{3+4k^{2}} and \frac{16k^{2}-48}{3+4k^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8k^{2}-\left(16k^{2}-48\right)}{3+4k^{2}}$$

Do the multiplications in 8k^{2}-\left(16k^{2}-48\right).

$$\frac{8k^{2}-16k^{2}+48}{3+4k^{2}}$$

Combine like terms in 8k^{2}-16k^{2}+48.

$$\frac{-8k^{2}+48}{3+4k^{2}}$$

Expand

$$-\frac{8\left(k^{2}-6\right)}{4k^{2}+3}$$

Short Solution Steps

Express 4\times \frac{4k^{2}-12}{3+4k^{2}} as a single fraction.

$$\frac{8k^{2}}{3+4k^{2}}-\frac{4\left(4k^{2}-12\right)}{3+4k^{2}}$$

Use the distributive property to multiply 4 by 4k^{2}-12.

$$\frac{8k^{2}}{3+4k^{2}}-\frac{16k^{2}-48}{3+4k^{2}}$$

Since \frac{8k^{2}}{3+4k^{2}} and \frac{16k^{2}-48}{3+4k^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8k^{2}-\left(16k^{2}-48\right)}{3+4k^{2}}$$

Do the multiplications in 8k^{2}-\left(16k^{2}-48\right).

$$\frac{8k^{2}-16k^{2}+48}{3+4k^{2}}$$

Combine like terms in 8k^{2}-16k^{2}+48.

$$\frac{-8k^{2}+48}{3+4k^{2}}$$