Solve 4-7k/1-6k(k-3)

$$4- \frac{ 7k }{ 1-6k } (k-3)$$

Evaluate

$$-\frac{\left(7k-4\right)\left(k+1\right)}{1-6k}$$

Short Solution Steps

Express \frac{7k}{1-6k}\left(k-3\right) as a single fraction.

$$4-\frac{7k\left(k-3\right)}{1-6k}$$

Use the distributive property to multiply 7k by k-3.

$$4-\frac{7k^{2}-21k}{1-6k}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{1-6k}{1-6k}.

$$\frac{4\left(1-6k\right)}{1-6k}-\frac{7k^{2}-21k}{1-6k}$$

Since \frac{4\left(1-6k\right)}{1-6k} and \frac{7k^{2}-21k}{1-6k} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(1-6k\right)-\left(7k^{2}-21k\right)}{1-6k}$$

Do the multiplications in 4\left(1-6k\right)-\left(7k^{2}-21k\right).

$$\frac{4-24k-7k^{2}+21k}{1-6k}$$

Combine like terms in 4-24k-7k^{2}+21k.

$$\frac{4-3k-7k^{2}}{1-6k}$$

Expand

$$\frac{4-3k-7k^{2}}{1-6k}$$

Short Solution Steps

Express \frac{7k}{1-6k}\left(k-3\right) as a single fraction.

$$4-\frac{7k\left(k-3\right)}{1-6k}$$

Use the distributive property to multiply 7k by k-3.

$$4-\frac{7k^{2}-21k}{1-6k}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{1-6k}{1-6k}.

$$\frac{4\left(1-6k\right)}{1-6k}-\frac{7k^{2}-21k}{1-6k}$$

Since \frac{4\left(1-6k\right)}{1-6k} and \frac{7k^{2}-21k}{1-6k} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(1-6k\right)-\left(7k^{2}-21k\right)}{1-6k}$$

Do the multiplications in 4\left(1-6k\right)-\left(7k^{2}-21k\right).

$$\frac{4-24k-7k^{2}+21k}{1-6k}$$

Combine like terms in 4-24k-7k^{2}+21k.

$$\frac{4-3k-7k^{2}}{1-6k}$$