Question

Solve the equation 8/x-4=9/6+x

Answer 1

`D:x\\ot =4 \wedge x\\ot=-6\\ (8)/(x-4)=(9)/(6+x)\\\\ 9(x-4)=8(6+x)\\ 9x-36=48+8x\\ x=84`

Answer 2

Solve by multiplying each side by the other side's denominator:


`(8)/(x - 4) = (9)/(6 + x)`

`8(6 + x) = 9(x - 4)`

`48 + 8x = 9x - 36`

`\bf x = 84`

Now, something you should always check when you have x in the denominator of a fraction is to make sure that there isn't a problem with division by 0. Since neither of the fractions has a denominator of 0 when x = 84, there's no issue, so we're safe.