SOLUTION: Hi, I actually have 2 questions relating to adding and subtracting fractions using variables.
1)x-y/x+y + x+y/x-y
I thought it was 1 but now it seems that would be too easy.
Question 5698: Hi, I actually have 2 questions relating to adding and subtracting fractions using variables.
1)x-y/x+y + x+y/x-y
I thought it was 1 but now it seems that would be too easy.
2) 1/x - 1/x+4 = 1/3
*I know I'm supposed to find the LCD and multiply both sides by it, but I'm not sure what that is.
You can put this solution on YOUR website! 1) You have to find the LCD which is (x+y)(x-y). Now you have to multiply each fraction with the missing term:
(x-y)(x-y)/(x+y)(x-y) + (x+y)(x+y)/(x-y)(x+y)
With a common denominator in both fractions we can rewrite as follows:
(x-y)(x-y)+(x+y)(x+y)/(x+y)(x-y) Now let's simplify the numerator
(x^2-2xy+y^2)+(x^2+2xy+y^2)/(x+y)(x-y) Combine like terms in the numerator
(2x^2+2y^2)/(x+y)(x-y)
This is already your final answer. You can factor out the 2 in the numerator and evaluate the denominator but it won't change the value.
2(x^2+y^2)/(x^2-y^2) The sum of two squares is not factorable unless there is a common factor.
2)Like you already said you have to find the LCD which is 3x(x+4) in this case. Let's look how we found the LCD. Look at every denominator: x , (x+4) , 3
The LCD contains each different (prime) factor the most times it appears. Thus 3x(x+4).Now we have to multiply each fraction(numerator and denominator) by the missing term to produces equivalent fractions with the same denominator.
1/x-1/(x+4) = 1/3
{1*3(x+4)}/{x*3(x+4) - {1*(3x)}/{(x+4)*3x} = {1*x(x+4)}/{3*x(x+4)}
A big advantage when computing equations with fractions is that by using the LCD you can clear the equation of all fractions.
3(x+4) - 3x = x(x+4) Simplify both sides
3x+12-3x = x²+4x Combine like terms
x²+4x-12=0 To solve this equation we have to factor out the GCF. First we need to find 2 numbers whose sum is 4 and whose product is -12. 6 and -2 satisfy options.
x²+6x-2x-12=0 Now we can factor out
x(x+6)-2(x+6)=0
(x-2)(x+6)=0
Solve for x
x-2=0, x=2
x+6=0, x=-6
Check:
1/2 - 1/(2+4) = 1/3
1/2 - 1/6 = 1/3
3-1 = 2, 2=2
and
1/(-6) - 1/(-6+4) = 1/3
1/(-6) - 1/(-2) = 1/3
-1+3=2, 2=2
Hope it helps
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