SOLUTION: Can someone please help me solve this problem?
2/5x+5 - 3/x^2-1 = 4/x-1
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Question 278133: Can someone please help me solve this problem?
2/5x+5 - 3/x^2-1 = 4/x-1
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Equations are easier if there are no fractions, I think you'll agree. So we'll start by eliminating the fractions. The asiest way to eliminate the fractions in an equation is to multiply both sides by the Lowest Common Denominator (LCD). And to find the LCD we need to factor the denominators:
The LCD is the product of all the different factors. So the LCD here is:
(5)(x+1)(x-1)
This is what we will multiply both sides by:
On the left side we need to use the Distributive Property:
Now we can cancel:
leaving:
(x-1)(2) - (5)3 = 5(x+1)4
which simplifies to:
2x - 2 - 15 = 20(x+1)
2x - 17 = 20x +20
Without the fractions, this is a very simple equation to solve. Subtract 2x from each side:
-17 = 18x + 20
Subtract 20 from each side:
-37 = 18x
Divide both sides by 18:
-37/18 = x
With equations where the variable is in one or more denominators, it is important to check your answers. We must make sure no denominators are zero! A quick mental check and you can see that -37/18 does not make any of the denominators zero. So that is out solution.
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