This is my problem: 3+3/x divided by 4+4/x. I am working on Khan Academy and got this question. My friend tried to help me work through it who is very good at math but I was just blanking out as she tried to explain it. I think I am missing a vital understanding of a step that is not explained in the hint/walk through on Khan Academy. Could someone help me walk through this step by step so that I can ask questions if I get lost? Any help would be appreciated. Thanks!
3+3/x divided by 4+4/x Explained
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lev888
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Is it a simplification problem? Convert both expressions into fractions. Replace division by multiplication by flipping the second fraction. Multiply the fractions.
HallsofIvy
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\(\displaystyle 3+ \frac{3}{x}= \frac{3x+ 3}{x}\) and \(\displaystyle 4+ \frac{4}{x}= \frac{4x+ 4}{x}\),
\(\displaystyle 3+ \frac{3}{x}\) divided by \(\displaystyle 4+ \frac{4}{x}\) is \(\displaystyle \frac{3x+ 3}{x}\frac{x}{4x+ 4}= \frac{3(x+ 1)}{4(x+ 1)}= \frac{3}{4}\)
\(\displaystyle 3+ \frac{3}{x}\) divided by \(\displaystyle 4+ \frac{4}{x}\) is \(\displaystyle \frac{3x+ 3}{x}\frac{x}{4x+ 4}= \frac{3(x+ 1)}{4(x+ 1)}= \frac{3}{4}\)
The question is just [MATH]\frac{3\left(1+\frac{1}{x}\right)}{4\left(1+\frac{1}{x}\right)}[/MATH]
which is [MATH] \frac{3}{4}[/MATH]
([MATH]x\neq0,\ x\neq-1[/MATH])