Question

Given that a=3, b=-2 and c= -4, evaluate the following expression. 2c-a/3c+b - 5a+4c/c-a

Answer 1

Given:

Consider the given expression is:

$\dfrac{2c-a}{3c+b}-\dfrac{5a+4c}{c-a}$

To find:

The value of the given expression for $a=3, b=-2, c=-4$.

Solution:

We have,

$\dfrac{2c-a}{3c+b}-\dfrac{5a+4c}{c-a}$

Substituting $a=3, b=-2, c=-4$, we get

$\dfrac{2(-4)-(3)}{3(-4)+(-2)}-\dfrac{5(3)+4(-4)}{(-4)-(3)}$

$=\dfrac{-8-3}{-12-2}-\dfrac{15-16}{-4-3}$

$=\dfrac{-11}{-14}-\dfrac{-1}{-7}$

$=\dfrac{11}{14}-\dfrac{1}{7}$

Taking LCM, we get

$=\dfrac{11-2}{14}$

$=\dfrac{9}{14}$

Therefore, the value of the given expression for $a=3, b=-2, c=-4$ is $\dfrac{9}{14}$.