Given:
Consider the given expression is:
[tex]\dfrac{2c-a}{3c+b}-\dfrac{5a+4c}{c-a}[/tex]
To find:
The value of the given expression for [tex]a=3, b=-2, c=-4[/tex].
Solution:
We have,
[tex]\dfrac{2c-a}{3c+b}-\dfrac{5a+4c}{c-a}[/tex]
Substituting [tex]a=3, b=-2, c=-4[/tex], we get
[tex]\dfrac{2(-4)-(3)}{3(-4)+(-2)}-\dfrac{5(3)+4(-4)}{(-4)-(3)}[/tex]
[tex]=\dfrac{-8-3}{-12-2}-\dfrac{15-16}{-4-3}[/tex]
[tex]=\dfrac{-11}{-14}-\dfrac{-1}{-7}[/tex]
[tex]=\dfrac{11}{14}-\dfrac{1}{7}[/tex]
Taking LCM, we get
[tex]=\dfrac{11-2}{14}[/tex]
[tex]=\dfrac{9}{14}[/tex]
Therefore, the value of the given expression for [tex]a=3, b=-2, c=-4[/tex] is [tex]\dfrac{9}{14}[/tex].
