SOLUTION: The numerator of a fraction is 1 less than the denominator. If the numerator and the denominator are both increased by 4, the new fraction will be 1/8 more than the original fract
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Question 136648This question is from textbook Algebra Structure and Method
: The numerator of a fraction is 1 less than the denominator. If the numerator and the denominator are both increased by 4, the new fraction will be 1/8 more than the original fraction. Find the original fraction.
This question is from textbook Algebra Structure and Method
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The numerator of a fraction is 1 less than the denominator. If the numerator and the denominator are both increased by 4, the new fraction will be 1/8 more than the original fraction. Find the original fraction.
:
Write an equation for what it says:
+ =
:
+ =
:
The common denominator will be 8(x+1)(x+5)
Multiply each term by this, cancel out the denominators, leaving us with:
x(8(x+5) + (x+1)(x+5) = 8(x+4)(x+1)
:
8x^2 + 40x + x^2 + 6x + 5 = 8(x^2 + 5x + 4)
:
8x^2 + 40x + x^2 + 6x + 5 = 8x^2 + 40x + 32
Combine on the left:
8x^2 + x^2 - 8x^2 + 40x + 6x - 40x + 5 - 32 = 0
A quadratic equation
x^2 + 6x - 27 = 0
Factors to:
(x+9)(x-3) = 0
We want the positive solution:
x = 3
:
Check solution in original equation
+ =
:
Actually the negative solution x = -9 will work also:
+ =
:
:
Did I make this understandable? Any questions?
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