Question

How do you solve `(x+5)/(x-1)=7/6`?

Answer 1

`x=37`

Explanation:

`"we can use "color(blue)"cross-multiplication ""to solve"`

`"given one fraction equal to another fraction then"`

`•color(white)(x)a/b=c/drArrad=bclarrcolor(blue)"cross-multiplication"`

`(x+5)/(x-1)=7/6`

`rArr7(x-1)=6(x+5)larrcolor(blue)"distribute"`

`rArr7x-7=6x+30`

`"subtract 6x from both sides"`

`7x-6x-7=cancel(6x)cancel(-6x)+30`

`rArrx-7=30`

`"add 7 to both sides"`

`xcancel(-7)cancel(+7)=30+7`

`color(blue)"As a check"`

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

`(37+5)/(37-1)=42/36=7/6=" right side"`

`rArrx=37" is the solution"`