Question

How do you solve rational equations `[(x+2) / (x-1)] = [1/2]`?

Answer 1

`x=-5`

Explanation:

When we have a fraction equal to another fraction we can use the method of `color(blue)"cross-multiplication"` to solve.

That is `(color(red)(x+2))/(color(blue)(x-1))=color(blue)(1)/color(red)(2)`

Now multiply the terms on either end of an 'imaginary' cross (X). That is multiply the `color(red)("red")` values together and the `color(blue)("blue")` values together and equate them.

`rArrcolor(red)(2(x+2))=color(blue)(1(x-1))`

distribute the brackets.

`rArr2x+4=x-1`

We now want to have the x terms on the left of the equation and numeric values on the right.

subtract x from both sides.

`2x-x+4=cancel(x)cancel(-x)-1`

`rArrx+4=-1`

subtract 4 from both sides.

`xcancel(+4)cancel(-4)=-1-4`

`rArrx=-5" is the solution"`