\[ If \frac{a}{b}=-\frac{2}{3},\ then \frac{b-a}{a} \]

VJesus12 wrote:$$If\ \ \ \frac{a}{b}=-\frac{2}{3},\ then\ \ \frac{b-a}{a}=\ ?$$ (A) − 5/2
(B) − 5/3
(C) − 1/3
(D) 0
(E) 7

The OA is the option A .

Could someone explain this PS question to me? I don't know how to solve it without finding the values of a and b. <i class="em em-cold_sweat"></i>

Hello Vjesus12.

It is not necessary to find the values of "a" and "b". Let's see how can we solve it.

We just have to rewrite the given expression and use that a/b = -2/3 as follows: $$\frac{b-a}{a}=\frac{b}{a}-\frac{a}{a}=\frac{1}{\frac{a}{b}}-1=\frac{1}{-\frac{2}{3}}-1=-\frac{3}{2}-1=-\frac{5}{2}.$$ Hence, we get the that the correct answer is the option A.

I hope it can help you. <i class="em em-grinning"></i>