Simplify (3z)/(5z-25)-(z+1)/(2z-10)

$\frac{3 z}{5 z - 25} - \frac{z + 1}{2 z - 10}$

Step 1

Simplify each term.

Factor $5$ out of $5 z - 25$ .

Factor $5$ out of $5 z$ .

$\frac{3 z}{5 (z) - 25} - \frac{z + 1}{2 z - 10}$

Factor $5$ out of $- 25$ .

$\frac{3 z}{5 z + 5 \cdot - 5} - \frac{z + 1}{2 z - 10}$

Factor $5$ out of $5 z + 5 \cdot - 5$ .

$\frac{3 z}{5 (z - 5)} - \frac{z + 1}{2 z - 10}$

Factor $2$ out of $2 z - 10$ .

Factor $2$ out of $2 z$ .

$\frac{3 z}{5 (z - 5)} - \frac{z + 1}{2 (z) - 10}$

Factor $2$ out of $- 10$ .

$\frac{3 z}{5 (z - 5)} - \frac{z + 1}{2 z + 2 \cdot - 5}$

Factor $2$ out of $2 z + 2 \cdot - 5$ .

$\frac{3 z}{5 (z - 5)} - \frac{z + 1}{2 (z - 5)}$

Step 2

To write $\frac{3 z}{5 (z - 5)}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 z}{5 (z - 5)} \cdot \frac{2}{2} - \frac{z + 1}{2 (z - 5)}$

Step 3

To write $- \frac{z + 1}{2 (z - 5)}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 z}{5 (z - 5)} \cdot \frac{2}{2} - \frac{z + 1}{2 (z - 5)} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $10 (z - 5)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 z}{5 (z - 5)}$ by $\frac{2}{2}$ .

$\frac{3 z \cdot 2}{5 (z - 5) \cdot 2} - \frac{z + 1}{2 (z - 5)} \cdot \frac{5}{5}$

Multiply $2$ by $5$ .

$\frac{3 z \cdot 2}{10 (z - 5)} - \frac{z + 1}{2 (z - 5)} \cdot \frac{5}{5}$

Multiply $\frac{z + 1}{2 (z - 5)}$ by $\frac{5}{5}$ .

$\frac{3 z \cdot 2}{10 (z - 5)} - \frac{(z + 1) \cdot 5}{2 (z - 5) \cdot 5}$

Multiply $5$ by $2$ .

$\frac{3 z \cdot 2}{10 (z - 5)} - \frac{(z + 1) \cdot 5}{10 (z - 5)}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 z \cdot 2 - (z + 1) \cdot 5}{10 (z - 5)}$

Step 6

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{6 z - (z + 1) \cdot 5}{10 (z - 5)}$

Apply the distributive property.

$\frac{6 z + (- z - 1 \cdot 1) \cdot 5}{10 (z - 5)}$

Multiply $- 1$ by $1$ .

$\frac{6 z + (- z - 1) \cdot 5}{10 (z - 5)}$

Apply the distributive property.

$\frac{6 z - z \cdot 5 - 1 \cdot 5}{10 (z - 5)}$

Multiply $5$ by $- 1$ .

$\frac{6 z - 5 z - 1 \cdot 5}{10 (z - 5)}$

Multiply $- 1$ by $5$ .

$\frac{6 z - 5 z - 5}{10 (z - 5)}$

Subtract $5 z$ from $6 z$ .

$\frac{z - 5}{10 (z - 5)}$

Step 7

Cancel the common factor of $z - 5$ .

Cancel the common factor.

$\frac{z - 5}{10 (z - 5)}$

Rewrite the expression.

$\frac{1}{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{10}$

Decimal Form:

$0.1$

Simplify (3z)/(5z-25)-(z+1)/(2z-10)

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