simplify each expression

Question

8x^2 -18/4x^2-10x+6

Answer 1

(8x²-18) / (4x²-10x+6)

 

     = 2(4x²-9) / 2(2x²-5x+3)

• (4x²-9) factors to (2x+3)(2x-3)
• 2x²-5x+3 factors to (2x-3)(x-1)  (use the "ac" method)

 

Substituting in the factors:

 

      = 2(2x+3)(2x-3) / 2(2x-3)(x-1)

 

Cancelling common terms in the numerator and denominator (2 and (2x-3)):

 

      = (2x+3) / (x-1)

 

Note that x cannot equal 1 or 3/2 as these make the denominator of the original expression equal to zero, which is undefined.