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Hi , so some algebra questions require that we divide by a variable . When can we do that safely ? my concern is that the value of the variable could be 0 ;we cannot divide by 0 . What if we are NOT told that the value is not 0 ? Can we still divide , assuming that it is not 0 ? here are an example that requires to divide by a variable , Source : Manhatten
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Hi , so some algebra questions require that we divide by a variable . When can we do that safely ? my concern is that the value of the variable could be 0 ;we cannot divide by 0 . What if we are NOT told that the value is not 0 ? Can we still divide , assuming that it is not 0 ? here are an example that requires to divide by a variable , Source : Manhatten
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Never reduce equation by a variable (or expression with variable), if you are not certain that the variable (or expression with the variable) doesn't equal to zero.
For the question at hand though neither x nor y can be 0 for two reasons:
We are given that \(xy^2 = -96\). If x or y were 0, then \(xy^2\) would be 0, not -96.
We are also given that \(\frac{1}{xy} = \frac{1}{24}\). If x or y were 0, then \(\frac{1}{xy}\) would be undefined and could not equal to 1/24.
SOLUTION:
If \(xy^2 = -96\) and \(\frac{1}{xy} = \frac{1}{24}\), what is y?
Multiply those two equations: \(xy^2*\frac{1}{xy} = -96*\frac{1}{24}\):
We are also given that 1xy=1241xy=124. If x or y were 0, then 1xy1xy would be undefined and could not equal to 1/24.
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so if we have a fraction , a variable in the denominator , we can assume safely that the denominator will NOT equal to 0 ? because then the fraction will be undefined For example : (x-2)/ x^2-4 = x-2 / (x+2)(x-2) now at this point , can we divide by x-2 ? ( neither we are told clearly that x cannot equal to 2 , nor we can conclude that info from the question as you did above)
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.