Solve 3(4/3-5)-4/frac{4{3-5x}}

$$\frac { 3 ( \frac { 4 } { 3 - 5 } ) - 4 } { \frac { 4 } { 3 - 5 x } }$$

Evaluate

$$\frac{25x-15}{2}$$

Solution Steps

Subtract 5 from 3 to get -2.

$$\frac{3\times \frac{4}{-2}-4}{\frac{4}{3-5x}}$$

Divide 4 by -2 to get -2.

$$\frac{3\left(-2\right)-4}{\frac{4}{3-5x}}$$

Multiply 3 and -2 to get -6.

$$\frac{-6-4}{\frac{4}{3-5x}}$$

Subtract 4 from -6 to get -10.

$$\frac{-10}{\frac{4}{3-5x}}$$

Divide -10 by \frac{4}{3-5x} by multiplying -10 by the reciprocal of \frac{4}{3-5x}.

$$\frac{-10\left(3-5x\right)}{4}$$

Divide -10\left(3-5x\right) by 4 to get -\frac{5}{2}\left(3-5x\right).

$$-\frac{5}{2}\left(3-5x\right)$$

Use the distributive property to multiply -\frac{5}{2} by 3-5x.

$$-\frac{5}{2}\times 3-\frac{5}{2}\left(-5\right)x$$

Express -\frac{5}{2}\times 3 as a single fraction.

$$\frac{-5\times 3}{2}-\frac{5}{2}\left(-5\right)x$$

Multiply -5 and 3 to get -15.

$$\frac{-15}{2}-\frac{5}{2}\left(-5\right)x$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$-\frac{15}{2}-\frac{5}{2}\left(-5\right)x$$

Express -\frac{5}{2}\left(-5\right) as a single fraction.

$$-\frac{15}{2}+\frac{-5\left(-5\right)}{2}x$$

Multiply -5 and -5 to get 25.

$$-\frac{15}{2}+\frac{25}{2}x$$

Expand

$$\frac{25x-15}{2}$$

Solution Steps

Subtract 5 from 3 to get -2.

$$\frac{3\times \frac{4}{-2}-4}{\frac{4}{3-5x}}$$

Divide 4 by -2 to get -2.

$$\frac{3\left(-2\right)-4}{\frac{4}{3-5x}}$$

Multiply 3 and -2 to get -6.

$$\frac{-6-4}{\frac{4}{3-5x}}$$

Subtract 4 from -6 to get -10.

$$\frac{-10}{\frac{4}{3-5x}}$$

Divide -10 by \frac{4}{3-5x} by multiplying -10 by the reciprocal of \frac{4}{3-5x}.

$$\frac{-10\left(3-5x\right)}{4}$$

Divide -10\left(3-5x\right) by 4 to get -\frac{5}{2}\left(3-5x\right).

$$-\frac{5}{2}\left(3-5x\right)$$

Use the distributive property to multiply -\frac{5}{2} by 3-5x.

$$-\frac{5}{2}\times 3-\frac{5}{2}\left(-5\right)x$$

Express -\frac{5}{2}\times 3 as a single fraction.

$$\frac{-5\times 3}{2}-\frac{5}{2}\left(-5\right)x$$

Multiply -5 and 3 to get -15.

$$\frac{-15}{2}-\frac{5}{2}\left(-5\right)x$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$-\frac{15}{2}-\frac{5}{2}\left(-5\right)x$$

Express -\frac{5}{2}\left(-5\right) as a single fraction.

$$-\frac{15}{2}+\frac{-5\left(-5\right)}{2}x$$

Multiply -5 and -5 to get 25.

$$-\frac{15}{2}+\frac{25}{2}x$$