common factors, how do i know which to cancel out?
- Thread starter bobisaka
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lev888
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Distribution follows this rule: a(b+c)=ab+ac.
Cancelling: (ab)/a = b. The order (ab or ba) doesn't matter.
Dr.Peterson
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You'll have to show how you canceled, in order for us to see if you made a mistake.
I think they made the distribution in the denominator obvious, but the canceling might be misunderstood, as they did a lot at once.
The only places they are canceling are within individual multiplications, one place in the numerator and two in the denominator. It helps many students if they rewrite the non-fractions as fractions. In the numerator, for example, we have [MATH](x+6)(x-6)\left(\frac{2}{x+6}\right) = \frac{x+6}{1}\frac{x-6}{1}\frac{2}{x+6}[/MATH], so the [MATH](x+6)[/MATH] in the numerator of the first fraction cancels with the [MATH](x+6)[/MATH] in the denominator in the last to leave [MATH](x-6)[/MATH] alone.
In general, when you have a product like [MATH]a\cdot\frac{b}{c}[/MATH], you can think of the [MATH]a[/MATH] "at ground level" and the [MATH]b[/MATH] "on the main floor" as at the same level, and the [MATH]c[/MATH] "in the basement" can cancel with either of the others. The product is equivalent to [MATH]\frac{ab}{c}[/MATH].