Simplify ((2a-b)/b+1)/((2a+b)/b-1)

$\frac{\frac{2 a - b}{b} + 1}{\frac{2 a + b}{b} - 1}$

Step 1

Multiply the numerator and denominator of the complex fraction by $b$ .

Multiply $\frac{\frac{2 a - b}{b} + 1}{\frac{2 a + b}{b} - 1}$ by $\frac{b}{b}$ .

$\frac{b}{b} \cdot \frac{\frac{2 a - b}{b} + 1}{\frac{2 a + b}{b} - 1}$

Combine.

$\frac{b (\frac{2 a - b}{b} + 1)}{b (\frac{2 a + b}{b} - 1)}$

Step 2

Apply the distributive property.

$\frac{b \frac{2 a - b}{b} + b \cdot 1}{b \frac{2 a + b}{b} + b \cdot - 1}$

Step 3

Simplify by cancelling.

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{b \frac{2 a - b}{b} + b \cdot 1}{b \frac{2 a + b}{b} + b \cdot - 1}$

Rewrite the expression.

$\frac{2 a - b + b \cdot 1}{b \frac{2 a + b}{b} + b \cdot - 1}$

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{2 a - b + b \cdot 1}{b \frac{2 a + b}{b} + b \cdot - 1}$

Rewrite the expression.

$\frac{2 a - b + b \cdot 1}{2 a + b + b \cdot - 1}$

Step 4

Simplify the numerator.

Multiply $b$ by $1$ .

$\frac{2 a - b + b}{2 a + b + b \cdot - 1}$

Add $- b$ and $b$ .

$\frac{2 a + 0}{2 a + b + b \cdot - 1}$

Add $2 a$ and $0$ .

$\frac{2 a}{2 a + b + b \cdot - 1}$

Step 5

Simplify the denominator.

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

$\frac{2 a}{2 a + b - 1 \cdot b}$

Rewrite $- 1 b$ as $- b$ .

$\frac{2 a}{2 a + b - b}$

Subtract $b$ from $b$ .

$\frac{2 a}{2 a + 0}$

Add $2 a$ and $0$ .

$\frac{2 a}{2 a}$

Step 6

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a}{2 a}$

Rewrite the expression.

$\frac{a}{a}$

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a}{a}$

Rewrite the expression.

$1$

Simplify ((2a-b)/b+1)/((2a+b)/b-1)

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