Question

If b = ${\displaystyle \frac{2\text{a}}{\text{a}-2}}$, and c = ${\displaystyle \frac{4\text{b}-3}{3\text{b}+4}}$, then express c in terms of a.

Answer 1

Given b = ${\displaystyle \frac{2\text{a}}{\text{a}-2},\text{and}\text{c}=\frac{4\text{b}-3}{3\text{b}+4}}$

Substituting b = ${\displaystyle \frac{2\text{a}}{\text{a}-2}\text{in c}=\frac{4\text{b}-3}{3\text{b}+4}}$

c = ${\displaystyle \frac{4\left(\frac{2\text{a}}{\text{a}-2}\right)-3}{3\left(\frac{2\text{a}}{\text{a}-2}\right)+4}}$

⇒ c = ${\displaystyle \frac{\frac{8\text{a}}{\text{a}-2}-3}{\frac{6\text{a}}{\text{a}-2}+4}}$

⇒ c = ${\displaystyle \frac{\frac{8\text{a}-3(\text{a}-2)}{\text{a}-2}}{\frac{6\text{a}+4(\text{a}-2)}{\text{a}-2}}}$

⇒ c = ${\displaystyle \frac{8\text{a}-3(\text{a}-2)}{6\text{a}+4(\text{a}-2)}}$

⇒ c = ${\displaystyle \frac{8\text{a}-3\text{a}+6}{6\text{a}+4\text{a}-8}}$

⇒ c = ${\displaystyle \frac{5\text{a}+6}{10\text{a}-8}}$.