Question

Solve for x:
$\frac{2x-a}{b} = \frac{ax+1}{c}, if ab\neq 2c$

Answer 1

$\huge{ \underline{ \underline \mathfrak \red{Answer \: : - }}}$

Given,

a/(x-a) + b/(x-c) = 2c/(x-c)

To find the value of x ,

Solution :-

a/(x-a) + b/(x-c) = 2c/(x-c)

⇒ a/(x-a) + b/(x-c) = c/(x-c) + c/(x-c)

⇒ a/(x-a) - c/(x-c) = c/(x-c) - b/(x-c)

⇒ a(x-c) - c(x-a) / (x-a) (x-c) = (c-b)/(x-c)

(x-c) cancel out from each side , we get,

⇒ ax - ac - cx + ac / (x-a) = (c-b)

⇒ ax - cx / (x-a) = (c-b)

⇒ (a-c)x = (c-b) (x-a)

⇒ (a-c)x = (c-b)x - a(c-b)

⇒ (a-c)x - (c-b)x = -a(c-b)

⇒ (a-c-c+b)x = -a(c-b)

⇒ (a+b-2c)x = a(b-c)

⇒ x = a(b-c) / (a+b-2c)

Answer 2

=>(a−c)x=(c−b)x−a(c−b)

= > (a - c)x - (c - b)x = - a(c - b)=>(a−c)x−(c−b)x=−a(c−b)

= > (a - c - c + b)x = - a(c - b)=>(a−c−c+b)x=−a(c−b)

$\begin{gathered}= > (a + b - 2c)x \: = a(b - c) \\ = > \: \: \: x \: \: \: = \dfrac{a(b - c)}{(a + b - 2c)}\end{gathered}$