SOLUTION: If 1/x + 1/a = 1/b then what is x

Algebra ->  Rational-functions -> SOLUTION: If 1/x + 1/a = 1/b then what is x      Log On


   

Question 118229: If 1/x + 1/a = 1/b then what is x
Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If 1%2Fx+%2B+1%2Fa+=+1%2Fb then what is x
1%2Fx+%2B+1%2Fa+=+1%2Fb..........multiply both sides by xab

%281%2Fx%29%28xab%29+%2B+%281%2Fa%29%28xab%29+=+%281%2Fb%29%28xab%29



ab+%2B+xb+=+xa......move ab to the rght and xato the left
xb-+%28xa%29+=+-%28ab%29......
x%28b-+a%29+=+-%28ab%29......
x+=+-%28ab%29%2F%28b-+a%29......

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx+%2B+1%2Fa+=+1%2Fb Start with the given equation


1%2Fx++=+1%2Fb+-+1%2Fa Subtract 1%2Fa from both sides


1%2Fx++=+%28a%2Fa%29%281%2Fb%29+-+%28b%2Fb%29%281%2Fa%29 Multiply 1%2Fb by a%2Fa. Multiply 1%2Fa by b%2Fb.


1%2Fx++=+a%2Fab+-+b%2Fab%29 Multiply.


1%2Fx++=+%28a-+b%29%2Fab Combine the fractions.


ab++=+x%28a-+b%29 Cross multiply


ab%2F%28a-+b%29+=+x Divide both sides by a-b


So our answer is x=ab%2F%28a-+b%29



note: the previous answer x=-ab%2F%28b-+a%29 is equivalent to x=ab%2F%28a-+b%29

-ab%2F%28b-+a%29 Start with any answer (I chose the previous answer)


%28-1%29ab%2F%28b-+a%29 Factor a -1 out of the numerator

%28-1%29ab%2F%28-1%29%28-b%2B+a%29 Factor a -1 out of the denominator


%28-1%29ab%2F%28-1%29%28a-b%29 Rearrange the terms


cross%28-1%29ab%2Fcross%28-1%29%28a-b%29 Divide and cancel out the "-1" terms


ab%2F%28a-b%29 Simplify


So this shows that ab%2F%28a-b%29=-ab%2F%28b-+a%29 which means either answer will work.