Question

solve 1/m=m-34/2m^2

Answer 1

\[\frac{ 1 }{ m }=m-\frac{ 34 }{ 2m ^{2} }\]
What is the LCD? Multiply all three terms by the LCD to eliminate the fractions. The resulting equation should be relatively easy to solve for m.

Answer 2

Why do they teach LCD, I don't really see the point, seems like they are over complicating something simple.

First off multiply both sides by 2m^2 so,

\[\frac{1}{m} = m - \frac{34}{2m^2}\]
\[2m^2(\frac{1}{m}) =( m - \frac{34}{2m^2})2m^2\]
\[2m^2(\frac{1}{m}) =(2m^2)m - \frac{34}{2m^2}\frac{2m^2}{1}\]
\[\frac{2m^2}{1}(\frac{1}{m}) =(2m^2)m - \frac{34*2m^2}{2m^2*1}\]
\[\frac{1*2m^2}{1*m} =(2m^2)m - \frac{34*2m^2}{2m^2*1}\]
\[\frac{1*2m^2}{m} =(2m^2)m - \frac{34*2m^2}{2m^2}\]

Answer 3

You can simplify this right?

Answer 4

I just showed 1 as the denominator for 2m^2 to show the fractional multiplication rule,

also notice I used distributive rule,

A(C + B) = A*C + A*B

Answer 5

Are we sure this isn't
\[\frac{1}m = \frac{m-34}{2m^2}\]?

Answer 6

even if it was it could still be solved the same way

Answer 7

Yes, but it could be more easily solved by cross-multiplication, with no need for any fraction tomfoolery.

Answer 8

two reasons I think my version is more likely:

1) why wouldn't they have factored out the common 2 in the fraction
2) the solution to this version is pretty ugly :-)

Answer 9

@whpalmer4 : I would agree with you IF and only if you combine the two expressions on the right side of the equation into one fraction; if you do that, you certainly can use cross multiplication. Otherwise, I'd beg to differ.

Answer 10

I don't think this guy is solving cubic equations, from what I remember of other questions asked.

Answer 11

@mathmale in my version there are no fractions to combine...it's just
\[\frac{1}m = \frac{m-34}{2m^2}\]

Answer 12

anyhow, you guys go ahead and solve the other one, I'm going to make popcorn and watch :-)

Answer 13

@whpalmer4 : So much depends on whether our friend @pjpkap has correctly typed the original problem here. More and more I urge participants to use Equation Editor for maximum clarity. If you and I end up with different interpretations of @pjpkap's problem, 1/m=m-34/2m^2, then it's time to go back to the source: @pjpkap and ask for clarification. Thanks for the thoughtful discussion (although we're both trying to defend our own points of view).

Answer 14

For fun, here's one of the 3 solutions to the cubic you all are working :-)

\[{m\to \frac{1}{3} \left(\frac{459}{2}-\frac{3 \sqrt{23397}}{2}\right)^{1/3}+\frac{\left(\frac{1}{2} \left(153+\sqrt{23397}\right)\right)^{1/3}}{3^{2/3}}}\]