Blog: {ab(a-b)(a-c)} / {ac(b-a)(b-c)}, Simplify.

Friday, January 1, 2016

$\displaystyle\frac{{{a}{b}{\left({a}-{b}\right)}{\left({a}-{c}\right)}}}{{{a}{c}{\left({b}-{a}\right)}{\left({b}-{c}\right)}}}$

They both share a on the top and bottom you should first divide by a to cancel out a, that would leave you:

$\displaystyle\frac{{{b}{\left({a}-{b}\right)}{\left({a}-{c}\right)}}}{{{c}{\left({b}-{a}\right)}{\left({b}-{c}\right)}}}$

Now switch the order of b-a to -a+b,

$\displaystyle\frac{{{b}{\left({a}-{b}\right)}{\left({a}-{c}\right)}}}{{{c}{\left(-{a}+{b}\right)}{\left({b}-{c}\right)}}}$

Now factor out a negative to make the denominator and the nominator the same:

$\displaystyle\frac{{{b}{\left({a}-{b}\right)}{\left({a}-{c}\right)}}}{{-{c}{\left({a}-{b}\right)}{\left({b}-{c}\right)}}}$

now divide by a-b to cancel them out

you should be left over with:

$\displaystyle\frac{{{b}{\left({a}-{c}\right)}}}{{-{c}{\left({b}-{c}\right)}}}$

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