Help with distributive property

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June 11th 2011, 08:17 PM
tcampbell011

Help with distributive property

Hey I was doing a math problem and needed help with one certain part near the end of the problem. Here is the problem and what I have done already:

8(1/x-7)=9(1/x)+3(1/5x)

8/x-7=9/x+3/5x

then I multiply each side by the least common denominator. I understand what to do on the left hand side, I just don't understand how to distribute the x-7 on the right (I assume the 5x gets canceled out:

5x(x-7)*(8/x-7) = (9/x+3/5x)*5x(x-7)

40x=(9/x+3)*(x-7)

Any help would be greatly appreciated!!!! I'm really frustrated! I know the answer is 48x-336 but I can't see how to get there!
June 11th 2011, 08:33 PM
Prove It

PLEASE use brackets where they're needed or learn some LaTeX, it's impossible to tell if you mean $\displaystyle \frac{1}{x - 7}$ or $\displaystyle \frac{1}{x} - 7$ , or if you mean $\displaystyle \frac{1}{5x}$ or $\displaystyle \frac{1}{5}x$ .

From your working, it looks like you meant

$\displaystyle \begin{align*}8\left(\frac{1}{x - 7} \right) &= 9\left(\frac{1}{x}\right) + 3\left(\frac{1}{5x}\right) \\ \frac{8}{x - 7} &= \frac{9}{x} + \frac{3}{5x} \\ \frac{8}{x - 7} &= \frac{45}{5x} + \frac{3}{5x} \\ \frac{8}{x - 7} &= \frac{48}{5x} \\ 8(5x) &= 48(x - 7) \\ 40x &= 48x - 336 \\ 336 &= 8x \\ 42 &= x \end{align*}$
June 11th 2011, 08:36 PM
tcampbell011

Thank you, I understand it now... I see how it could be confusing, but you nailed it. I will try to figure out what LaTeX is.