SOLUTION: Can someone help me please? 5/4x+1/8x=9/8+x the solution is x=? Im not very good at fractions they confuse me any help will be appreciated. Thanks

Question 249612: Can someone help me please?
5/4x+1/8x=9/8+x
the solution is x=?
Im not very good at fractions they confuse me any help will be appreciated. Thanks
Found 2 solutions by checkley77, dabanfield:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
5/4x+1/8x=9/8+x
5x/4+x/8-x=9/8 combine the x terms by finding a common denominator.
(5x*2+x-8*x)/8=9/8 combine the x terms.
(10x+x-8x)/8=9/8 cancel out the denominators & add the x terms.
3x=9
x=9/3=3 ans.
Proof:
5*3/4+3/8=9/8+3
15/4+3/8=9/8+24/8
30/8+3/8=33/8
33/8=33/8

Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
Can someone help me please?
5/4x+1/8x=9/8+x
the solution is x=?
Im not very good at fractions they confuse me any help will be appreciated. Thanks
To make things simpler let's rewrite the equation as:
(5/4x)+(1/8x)-9/(8+x) = 0
You first need to get all the fractions on the left side to have the same denominator. Then you can combine their numerators over that commmon denominator. Remember a/d + b/d + c/d = (a+b+c)/d
The easiest way to create a common denominator is to multiply all the denominators together. In this case that would be (4x)*(8x)*(8+x).
When we multiply the first term, 5/(4x), by ((8x)*(8+x))/((8x)*(8+x))which is actually equal to 1 we get:
(1.) (5*(8x)*(8+x))/((4x)*(8x)*(8+x))
Notice we have the common multiple we created above for the denominator now.
We can then multiply the second term, 1/(8x), by ((4x)*(8+x))/((4x)*(8+x)) which is also equal to 1 giving:
(2.) ((1*(4x)*(8+x)))/((4x)*(8x)*(8+x))
The second term now has the same denomininator as the first.
We can then multiply the third term, 9/(8+x), by ((4x)*8x))/((4x)*(8x)) which is also equal to 1 giving:
(3.) (9*4x*8x)/(4x*8x*(8+x))
Now you can combine the 3 numerators in (1.) (2.) and (3.) over the commmon denominator. You can then multiply the both sides of the resulting equation by the common denominator. The right side of the equation was 0 so multiplying it by the common denominator will still be 0. So in effect you have cleared the fractions. Remember if (a+b+c)/d = 0 then multipiiyng both sides by d will result in
a+b+c = 0
Combine and simplify the terms on the left side and then solve for x. Remember 0 or -8 cannot be solutions for the original equations since 4/x, 8/x and 1/(8+x) would be undefined.

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