SOLUTION: Determine x in the following: b/a - dx/c = ax/b - c/d. lcd = acbd bcd/a - dxab/c = axcd/b - acbx/d Unsure how to continue. Thanks.

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Question 1055682: Determine x in the following:
b/a - dx/c = ax/b - c/d.
lcd = acbd
bcd/a - dxab/c = axcd/b - acbx/d
Unsure how to continue. Thanks.

Found 3 solutions by Fombitz, josgarithmetic, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You didn't really need the LCD to start.
X terms on one side.
Constant terms on the other.
b%2Fa+-+%28d%2Fc%29x+=+%28a%2Fb%29x+-+c%2Fd
%28a%2Fb%29x%2B%28d%2Fc%29x=b%2Fa%2Bc%2Fd
%28a%2Fb%2Bd%2Fc%29x=b%2Fa%2Bc%2Fd
x=%28b%2Fa%2Bc%2Fd%29%2F%28a%2Fb%2Bd%2Fc%29
Now multiply numerator and denominator by the LCD.



Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Simplest common denominator is abcd.

abcd%28b%2Fa-dx%2Fc%29=abcd%28ax%2Fb-c%2Fd%29

b%5E2cd-abd%5E2x=a%5E2cdx-abc%5E2

-a%5E2cdx%2Bb%5E2cd-abd%5E2x=-abc%5E2

-a%5E2cdx-abd%5E2x%2Bb%5E2cd=-abc%5E2

multiply members by negative 1.
a%5E2cdx%2Babd%5E2x-b%5E2cd=abc%5E2

%28a%5E2cd%2Babd%5E2%29x-b%5E2cd=abc%5E2
You finish from here.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Determine x in the following:
b/a - dx/c = ax/b - c/d.
lcd = acbd
bcd/a - dxab/c = axcd/b - acbx/d
Unsure how to continue. Thanks.
b%2Fa+-+dx%2Fc+=+ax%2Fb+-+c%2Fd

Yes, LCD is abcd

b(bcd) - dx(abd) = ax(acd) - c(abc) -------- Multiplying by LCD, abcd

b%5E2cd+-+abd%5E2x+=+a%5E2cdx+-+abc%5E2

abc%5E2+%2B+b%5E2cd+-+abd%5E2x+=+a%5E2cdx ------- Adding abc%5E2 to both sides

abc%5E2+%2B+b%5E2cd+=+a%5E2cdx+%2B+abd%5E2x ------- Adding abd%5E2x to both sides

abc%5E2+%2B+b%5E2cd+=+x%28a%5E2cd+%2B+abd%5E2%29