Basic Math Examples

$\frac{8 t + z}{1 - t} - \frac{t - 3 z}{t - 1}$

Step 1

Factor $- 1$ out of $t$ .

$\frac{8 t + z}{1 - t} - \frac{t - 3 z}{- 1 (- t) - 1}$

Step 2

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{8 t + z}{1 - t} - \frac{t - 3 z}{- 1 (- t) - 1 (1)}$

Step 3

Factor $- 1$ out of $- 1 (- t) - 1 (1)$ .

$\frac{8 t + z}{1 - t} - \frac{t - 3 z}{- 1 (- t + 1)}$

Step 4

Reorder terms.

$\frac{8 t + z}{- t + 1} - \frac{t - 3 z}{- 1 (- t + 1)}$

Step 5

To write $\frac{8 t + z}{- t + 1}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{8 t + z}{- t + 1} \cdot \frac{- 1}{- 1} - \frac{t - 3 z}{- 1 (- t + 1)}$

Step 6

Write each expression with a common denominator of $(- t + 1) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{8 t + z}{- t + 1}$ by $\frac{- 1}{- 1}$ .

$\frac{(8 t + z) \cdot - 1}{(- t + 1) \cdot - 1} - \frac{t - 3 z}{- 1 (- t + 1)}$

Step 6.2

Reorder the factors of $(- t + 1) \cdot - 1$ .

$\frac{(8 t + z) \cdot - 1}{- (- t + 1)} - \frac{t - 3 z}{- 1 (- t + 1)}$

Step 7

Combine the numerators over the common denominator.

$\frac{(8 t + z) \cdot - 1 - (t - 3 z)}{- (- t + 1)}$

Step 8

Simplify the numerator.

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Step 8.1

Apply the distributive property.

$\frac{8 t \cdot - 1 + z \cdot - 1 - (t - 3 z)}{- (- t + 1)}$

Step 8.2

Multiply $- 1$ by $8$ .

$\frac{- 8 t + z \cdot - 1 - (t - 3 z)}{- (- t + 1)}$

Step 8.3

Move $- 1$ to the left of $z$ .

$\frac{- 8 t - 1 \cdot z - (t - 3 z)}{- (- t + 1)}$

Step 8.4

Rewrite $- 1 z$ as $- z$ .

$\frac{- 8 t - z - (t - 3 z)}{- (- t + 1)}$

Step 8.5

Apply the distributive property.

$\frac{- 8 t - z - t - (- 3 z)}{- (- t + 1)}$

Step 8.6

Multiply $- 3$ by $- 1$ .

$\frac{- 8 t - z - t + 3 z}{- (- t + 1)}$

Step 8.7

Subtract $t$ from $- 8 t$ .

$\frac{- 9 t - z + 3 z}{- (- t + 1)}$

Step 8.8

Add $- z$ and $3 z$ .

$\frac{- 9 t + 2 z}{- (- t + 1)}$

Step 9

Simplify terms.

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Step 9.1

Move the negative in front of the fraction.

$- \frac{- 9 t + 2 z}{- t + 1}$

Step 9.2

Factor $- 1$ out of $- 9 t$ .

$- \frac{- (9 t) + 2 z}{- t + 1}$

Step 9.3

Factor $- 1$ out of $2 z$ .

$- \frac{- (9 t) - (- 2 z)}{- t + 1}$

Step 9.4

Factor $- 1$ out of $- (9 t) - (- 2 z)$ .

$- \frac{- (9 t - 2 z)}{- t + 1}$

Step 9.5

Rewrite $- (9 t - 2 z)$ as $- 1 (9 t - 2 z)$ .

$- \frac{- 1 (9 t - 2 z)}{- t + 1}$

Step 9.6

Factor $- 1$ out of $- t$ .

$- \frac{- 1 (9 t - 2 z)}{- (t) + 1}$

Step 9.7

Rewrite $1$ as $- 1 (- 1)$ .

$- \frac{- 1 (9 t - 2 z)}{- (t) - 1 (- 1)}$

Step 9.8

Factor $- 1$ out of $- (t) - 1 (- 1)$ .

$- \frac{- 1 (9 t - 2 z)}{- (t - 1)}$

Step 9.9

Rewrite $- (t - 1)$ as $- 1 (t - 1)$ .

$- \frac{- 1 (9 t - 2 z)}{- 1 (t - 1)}$

Step 9.10

Cancel the common factor.

$- \frac{- 1 (9 t - 2 z)}{- 1 (t - 1)}$

Step 9.11

Rewrite the expression.

$- \frac{9 t - 2 z}{t - 1}$