Question

If $\frac{a}{b}=\frac{9}{5}$, then what is the value of $(2a + b)\div{(a-b)}?$

• A. $$\frac{19}{4}$$
• B. $$\frac{23}{5}$$
• C. $$\frac{23}{4}$$
• D. Cannot be determined

Answer 1

Answer:

$$\frac{23}{4}$$

Given:

$\frac{a}{b}=\frac{9}{5}$

Calculation:

$a=\frac{9b}{5}$

$(2a+b)\div{(a-b)}$

$⇒\frac{2\times{\frac{9b}{5}+b}}{\frac{9b}{5}-b}$

$⇒\frac{\frac{18b+5b}{5}}{\frac{9b-5b}{5}}$

$⇒\frac{23b}{4b}=\frac{23}{4}$

∴ The value of (2a + b) $\div{(a-b) }$is $\frac{23}{4}$