Question 78117: Please help me solve this one, I have worked on it for some time and cannot figure it out.
2x/9-5x/4=7/36
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 
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One of the ways you can approach this problem is to get rid of the denominators. Do this
by finding a number that is divisible by each of the three denominators. For this problem
the denominators are 9, 4, and 36. A number that is divisible by each of these numbers
is 36. (9 goes into 36 four times, 4 goes into 36 nine times, and 36 goes into 36 one time.)
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Next multiply every term in the given equation by 36. This makes your problem become:
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In the first term, the 9 of the denominator goes into the 36 in the numerator 4 times.
So cancel the 9 in the denominator and change the 36 in the numerator to 4.
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In the second term, the 4 of the denominator goes into the 36 in the numerator 9 times. So
cancel the 4 in the denominator and change the 36 in the numerator to 9.
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And finally, on the right side of the equal sign, the 36 of the denominator goes into the
36 of the numerator 1 time. So cancel the 36 in the denominator and replace the 36 in the
numerator with 1.
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When you do these three cancellations, the equation reduces to:
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Next do the multiplications to get:
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Add the two terms on the left side and you get:
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Finally, solve for just x by dividing both sides by the multiplier of x ... that is, divide
both sides by -37 to get:
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That's the answer to the problem. Hope this helps to give you some insight into eliminating
denominators in problems that have terms in fractional form. Find a number that has all
the denominators as factors and then multiply every term on both sides by that number.
After that, cancel the denominator of each fraction, but in the numerator replace the
common multiplier with the number obtained by dividing that terms denominator into the
common multiplier. Once you do that, what remains is just an equation with no denominators
and you can solve it just as you would any other equation.
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