How do I solve the following?

Question

  8   + x - 8 =    10     

x - 1      9        x - 1

 

Answer 1

The first thing you want to do is eliminate the denominators. This is done by multiplying each term by the Least Common Denominator (LCD) of the equation. 

 

For this one, the LCD is 9*(x-1). Multiplying each term by that gives  8*9 + (x-1)*(x-8) = 10*9

 

From here, we can multiply everything out and simplify it to:

 

72 + x² -9x + 8 = 90

 

x² - 9x + 80 = 90

 

we then subtract 90 from both sides to set it equal to 0 in order to factor it

 

x² - 9x - 10 = 0

 

(x-10)(x+1) = 0

 

gives us answers of x = 10 and x = -1

 

You can then plug these answers into the original to verify they work