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# Multiplying both sides of an equation...?

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Yo, guys, so here's the deal... if both sides of an equation are fractions with 8 being the denominator, is it fine to multiply both sides by 8 so it's easier to work with? Is that how math works...? Also, in case you were wondering, the equation I'm dealing with is...
3+((sqrt(256+16k))/8)=3(3-((sqrt(256+16k))/8))
Help is much appreciated, of course.

Nov 16, 2016

#2
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In order to eliminate the denominator in an equation, you must get it so that every item in said equation has the same denominator. Since the right side of the equation does not have a common denominator, multiplying by 8 would not work in this case. If you multiplied out the right side and got a common denominator, then multiplying by 8 would work.

Also yes, multiplying both sides by the SAME number doesn't change the solution of an equation, provided you've done it correctly. For example take x = 1. Multiplying both sides by 8 would give 8x = 8, and x = 1 same as before. Hope this helped.

Nov 16, 2016

#1
+5

No because of the problem being of two terms on both sides (or the addition of 3 and subtracting from 3) lf you multiplied both sides by 8 you would get 24 for those constants. l'm not totally sure if l'm correct. Your safest bet would be to put one side of the expression on the other through subtraction to make the entire thing equal zero.

Like so:

3+((sqrt(256+16k))/8) - 3(3-((sqrt(256+16k))/8)) = 0

Nov 16, 2016
#2
+5

In order to eliminate the denominator in an equation, you must get it so that every item in said equation has the same denominator. Since the right side of the equation does not have a common denominator, multiplying by 8 would not work in this case. If you multiplied out the right side and got a common denominator, then multiplying by 8 would work.

Also yes, multiplying both sides by the SAME number doesn't change the solution of an equation, provided you've done it correctly. For example take x = 1. Multiplying both sides by 8 would give 8x = 8, and x = 1 same as before. Hope this helped.

Guest Nov 16, 2016
#3
+5

Alright, thanks for the help lads. I think I've got it down now.

Nov 16, 2016