Question 71396: Combine: (3/x(to the 2nd) + 3x - 4) - (4/x(to the 2nd) - 6x - 40)
Please show work and solution Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Combine
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One of the first thing you can do is remove the parentheses by using the rules:
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(1) If a set of parentheses is preceded by a plus sign (no sign at all is assumed to be plus),
then just remove the parentheses without making changes to the terms within the parentheses.
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(2) If a set of parentheses is preceded by a minus sign you can remove the parentheses,
but you must change the signs of the terms within the parentheses. (A term that was plus
when it was within the parentheses becomes minus when the parentheses are removed. And a term
that was minus when it was within the parentheses becomes plus when the parentheses
are removed.)
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Note that the first set of parentheses (reading from left to right) does not have a
sign preceding it. Therefore, it is presumed to have a preceding plus sign and you can
remove the parentheses with out changing terms. This makes the problem:
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The remaining set of parentheses is preceded by a minus sign. Therefore, when you remove
the parentheses you must also change the sign of the three terms inside. When you do
this the problem becomes:
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Notice that the +3x and the +6x can be added to give +9x. Notice also that the -4 and
the +40 can be added to get + 36. Make these two substitutions to make the problem
become:
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Now notice that you have two fractions left to deal with. They both have the same
denominator so their numerators can be added and the resulting term put over the common
denominator. Their numerators are +3 and -4. When you add them the answer is -1 and
this is put over the common denominator to get . When you substitute
this into the equation, the result is:
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As far as I'm concerned, that answer is correct. However, maybe your teacher wants
everything over the common denominator of . If so, multiply the
by and you get and then multiply the by
and you get . Now all the terms have the common denominator of
so you can add their numerators and get and as a
final
touch you can arrange the numerator in descending powers of x so that the answer is:
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Check all the math above. It's pretty early in the morning and I haven't had a chance to
become fully awake. Feel free to correct any careless mistakes you find. I hope this
problem helps you to become familiar with some of the ways you can simplify algebraic
expressions.
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