Question

How do you solve `\frac { x - 3} { 2x - 4} = \frac { x } { x - 2} + 2`?

Answer 1

`x=1`

Explanation:

Solving the rational equation is computed by finding same denominator for denominators in both sides of the equation

Then,
`if color(red)(a/c=b/c` then `color(red)(a=c`

Then common denominator is the `L.C.M(2x-4,x-2)`
`color(blue)(2x-4=2(x-2)`
then `color(blue)(2x-4)` is the common denominator

`rArr(x-3)/(2x-4)=(color(blue)2x)/(color(blue)2(x-2))+(2xxcolor(blue)(2(x-2)))/color(blue)(2(x-2))`

`rArr(x-3)/(2x-4)=(2x+4(x-2))/(2x-4)`

`rArr(x-3)/(2x-4)=(2x+4x-8)/(2x-4)`

`rArr(x-3)/(2x-4)=(6x-8)/(2x-4)`

Then
`color(red)(x-3=6x-8)`

`rArrx-6x=3-8`

`rArr-5x=-5`
`rArrx=(-1)/(-1)`

Therefore, `x=1`