Question 74919
{{{1/40 + 1/(x+10) = 1/y}}}
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One method is to look at the denominators of the three terms in this equation. The denominators
are 40, (x+10), and y.  Suppose we made a product of all three of these ... that product
being 40*(x+10)*y.  Next suppose we multiplied this product times all three of the terms in 
the equation. This will get rid of all the denominators as shown below:
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{{{(1/40)*(40*(x+10)*y)+ (1/(x+10))*(40*(x+10)*y) = (1/y)*(40*(x+10)*y)}}}
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Now cancel the common terms in the numerators and denominators:
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{{{(1/cross(40))*(cross(40)*(x+10)*y)+ (1/cross(x+10))*(40*cross(x+10)*y) = (1/cross(y))*(40*(x+10)*cross(y))}}}
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What you are then left with is:
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{{{((x+10)*y) + 40*y = 40*(x+10)}}}
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Multiply out the left side to get:
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{{{xy + 10*y +40*y = 40*(x+10)}}}.
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Factor the common y out on the left side:
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{{{y*(x + 10 + 40)= 40*(x+10)}}}
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combine the 10 and the 40 on the left side:
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{{{y*(x+50) = 40*(x+10)}}}
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divide both sides by {{{(x+50)}}} and you get:
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{{{y = (40*(x+10))/(x+50)}}}
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That may be as far as you want to go. Maybe you can multiply out the numerator, but that's 
about it.
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Your second problem is almost the same, and you can use the above technique.
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{{{1/60 + 1/x = 1/y}}}
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Multiply all the terms in this equation by 60*x*y, the product of the three denominators.
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When you do that and cancel like terms in the numerators and denominators you get:
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{{{(xy) + 60y = 60*x}}}
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On the left side, factor the common y to get:
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{{{y*(x+60) = 60*x}}}
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divide both sides by {{{(x+60)}}} and you end up with:
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{{{y = (60*x/(x+60))}}}
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Hope this helps you.  Multiplying every term on both sides by a common denominator
enables you to eliminate the denominators entirely, and then you can work what's left just
as you would an ordinary equation. I hope the form of the answers above reflects what you were
asked to do ... namely solve for y in terms of x.