SOLUTION: Solve: (5x-8)/(x+2) = (5x-1)/(x+3)

Question 27277: Solve:
(5x-8)/(x+2) = (5x-1)/(x+3)

Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
Solve:
(5x-8)/(x+2) = (5x-1)/(x+3)----(1)
Cross multiplying
(5x-8)(x+3) = (5x-1)(x+2)
Expanding on the left as well as on the right
5x(x+3)- 8(x + 3) = 5x(x+2) - 1(x+2)
5x^2 + 15x - 8x -24 = 5x^2 + 10x - x -2
Subracting 5x^2 from both the sides(or cancelling 5x^2 on both the sides)
(15x - 8x) - 24 = (10x - x) - 2
7x - 24 = 9x -2
-24 + 2 = 9x - 7x
-22 = 2x
Dividing by 2
-11 = x
Answer: x = -11
Note: Since division by zero is not allowed,
the factors (x+3) and (x+2) in the dr on the left and right respectively indicate that x cannot be -3 and x cannot be -2
Verification:
Putting x = -11 in (1(
LHS = (5x-8)/(x+2) = [5 X (-11) - 8]/(-11+2) = (-55-8)/(-9) = -63/-9 = 7 ----*
RHS = (5x-1)/(x+3) = [5 X (-11) - 1]/(-11+3) = (-55-1)/(-8) = -56/-8 = 7 ----**
From * and ** we have x = -11 satisfying the given equation
Hence x=-11
Note: How is expansion carried out?
It is as follows:
Multiply the first term of the first bracket(including the sign) with the whole of the second bracket and then write the second term of the first bracket(including the sign)multiplied by the whole of the next bracket and continue similarly if there are more terms in the first bracket until all the terms in the first bracket are exhausted.

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