Simplify (7z-28)/(8-2z)

$\frac{7 z - 28}{8 - 2 z}$

Step 1

Simplify terms.

Factor $7$ out of $7 z - 28$ .

Factor $7$ out of $7 z$ .

$\frac{7 (z) - 28}{8 - 2 z}$

Factor $7$ out of $- 28$ .

$\frac{7 z + 7 \cdot - 4}{8 - 2 z}$

Factor $7$ out of $7 z + 7 \cdot - 4$ .

$\frac{7 (z - 4)}{8 - 2 z}$

$\frac{7 (z - 4)}{8 - 2 z}$

Factor $2$ out of $8 - 2 z$ .

Factor $2$ out of $8$ .

$\frac{7 (z - 4)}{2 (4) - 2 z}$

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

$\frac{7 (z - 4)}{2 (4) + 2 (- z)}$

Factor $2$ out of $2 (4) + 2 (- z)$ .

$\frac{7 (z - 4)}{2 (4 - z)}$

$\frac{7 (z - 4)}{2 (4 - z)}$

Cancel the common factor of $z - 4$ and $4 - z$ .

Factor $- 1$ out of $z$ .

$\frac{7 (- 1 (- z) - 4)}{2 (4 - z)}$

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{7 (- 1 (- z) - 1 (4))}{2 (4 - z)}$

Factor $- 1$ out of $- 1 (- z) - 1 (4)$ .

$\frac{7 (- 1 (- z + 4))}{2 (4 - z)}$

Reorder terms.

$\frac{7 (- 1 (- z + 4))}{2 (- z + 4)}$

Cancel the common factor.

$\frac{7 (- 1 (- z + 4))}{2 (- z + 4)}$

Rewrite the expression.

$\frac{7 \cdot (- 1)}{2}$

$\frac{7 \cdot (- 1)}{2}$

$\frac{7 \cdot (- 1)}{2}$

Step 2

Multiply $7$ by $- 1$ .

$\frac{- 7}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{7}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{2}$

Decimal Form:

$- 3.5$

Mixed Number Form:

$- 3 \frac{1}{2}$

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