Solve 4-2:(z-9)*(-3)+5-4*(2+3)

$$4 - 2 : ( z - 9 ) \cdot ( - 3 ) + 5 - 4 \cdot ( 2 + 3 )$$

Evaluate

$$\frac{105-11z}{z-9}$$

Short Solution Steps

Express \frac{2}{z-9}\left(-3\right) as a single fraction.

$$4-\frac{-2\times 3}{z-9}+5-4\left(2+3\right)$$

Multiply -2 and 3 to get -6.

$$4-\frac{-6}{z-9}+5-4\left(2+3\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{z-9}{z-9}.

$$\frac{4\left(z-9\right)}{z-9}-\frac{-6}{z-9}+5-4\left(2+3\right)$$

Since \frac{4\left(z-9\right)}{z-9} and \frac{-6}{z-9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(z-9\right)-\left(-6\right)}{z-9}+5-4\left(2+3\right)$$

Do the multiplications in 4\left(z-9\right)-\left(-6\right).

$$\frac{4z-36+6}{z-9}+5-4\left(2+3\right)$$

Combine like terms in 4z-36+6.

$$\frac{4z-30}{z-9}+5-4\left(2+3\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{z-9}{z-9}.

$$\frac{4z-30}{z-9}+\frac{5\left(z-9\right)}{z-9}-4\left(2+3\right)$$

Since \frac{4z-30}{z-9} and \frac{5\left(z-9\right)}{z-9} have the same denominator, add them by adding their numerators.

$$\frac{4z-30+5\left(z-9\right)}{z-9}-4\left(2+3\right)$$

Do the multiplications in 4z-30+5\left(z-9\right).

$$\frac{4z-30+5z-45}{z-9}-4\left(2+3\right)$$

Combine like terms in 4z-30+5z-45.

$$\frac{9z-75}{z-9}-4\left(2+3\right)$$

Add 2 and 3 to get 5.

$$\frac{9z-75}{z-9}-4\times 5$$

Multiply 4 and 5 to get 20.

$$\frac{9z-75}{z-9}-20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 20 times \frac{z-9}{z-9}.

$$\frac{9z-75}{z-9}-\frac{20\left(z-9\right)}{z-9}$$

Since \frac{9z-75}{z-9} and \frac{20\left(z-9\right)}{z-9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9z-75-20\left(z-9\right)}{z-9}$$

Do the multiplications in 9z-75-20\left(z-9\right).

$$\frac{9z-75-20z+180}{z-9}$$

Combine like terms in 9z-75-20z+180.

$$\frac{-11z+105}{z-9}$$

Expand

$$\frac{105-11z}{z-9}$$

Short Solution Steps

Express \frac{2}{z-9}\left(-3\right) as a single fraction.

$$4-\frac{-2\times 3}{z-9}+5-4\left(2+3\right)$$

Multiply -2 and 3 to get -6.

$$4-\frac{-6}{z-9}+5-4\left(2+3\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{z-9}{z-9}.

$$\frac{4\left(z-9\right)}{z-9}-\frac{-6}{z-9}+5-4\left(2+3\right)$$

Since \frac{4\left(z-9\right)}{z-9} and \frac{-6}{z-9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(z-9\right)-\left(-6\right)}{z-9}+5-4\left(2+3\right)$$

Do the multiplications in 4\left(z-9\right)-\left(-6\right).

$$\frac{4z-36+6}{z-9}+5-4\left(2+3\right)$$

Combine like terms in 4z-36+6.

$$\frac{4z-30}{z-9}+5-4\left(2+3\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{z-9}{z-9}.

$$\frac{4z-30}{z-9}+\frac{5\left(z-9\right)}{z-9}-4\left(2+3\right)$$

Since \frac{4z-30}{z-9} and \frac{5\left(z-9\right)}{z-9} have the same denominator, add them by adding their numerators.

$$\frac{4z-30+5\left(z-9\right)}{z-9}-4\left(2+3\right)$$

Do the multiplications in 4z-30+5\left(z-9\right).

$$\frac{4z-30+5z-45}{z-9}-4\left(2+3\right)$$

Combine like terms in 4z-30+5z-45.

$$\frac{9z-75}{z-9}-4\left(2+3\right)$$

Add 2 and 3 to get 5.

$$\frac{9z-75}{z-9}-4\times 5$$

Multiply 4 and 5 to get 20.

$$\frac{9z-75}{z-9}-20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 20 times \frac{z-9}{z-9}.

$$\frac{9z-75}{z-9}-\frac{20\left(z-9\right)}{z-9}$$

Since \frac{9z-75}{z-9} and \frac{20\left(z-9\right)}{z-9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9z-75-20\left(z-9\right)}{z-9}$$

Do the multiplications in 9z-75-20\left(z-9\right).

$$\frac{9z-75-20z+180}{z-9}$$

Combine like terms in 9z-75-20z+180.

$$\frac{-11z+105}{z-9}$$