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

4 Answers

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First of all, note that you have the same letter "a" at numerator and denominator, same time, so you can simplify it. The result will be:


After that, multiply the fraction with "-1" value so that, at numerator, (a-b) will become (b-a). But, note that (b-a) paranthesys is also at denominator, so you can simplify it too. The result will be, after simplifying action:


atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

`{ab(a-b)(a-c)} / {ac(b-a)(b-c)}`

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

`(b(a-b)(a-c)) / (c(b-a)(b-c))`

Now switch the order of b-a to -a+b, 

`(b(a-b)(a-c))/ (c(-a+b)(b-c))`

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

`(b(a-b)(a-c))/ (-c(a-b)(b-c))`

now divide by a-b to cancel them out

you should be left over with:


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revolution | College Teacher | (Level 1) Valedictorian

Posted on

{ab(a-b)(a-c)} / {ac(b-a)(b-c)}

First, divide this equation throughout by (a), as a is present in both side, so it turns out to be:

(b(a-b)(a-c)) / (c(b-a)(b-c))

Then, change (a-b) into (b-a), to be in the same form as the denominator Remember to put the negative sign in front of the numerator:

-(b(b-a)(a-c))/ (c(b-a)(b-c))

Divide b-a throughout top and bottom

-(b(a-c))/(c(b-c)) //


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neela | High School Teacher | (Level 3) Valedictorian

Posted on

To simplify {ab(a-b)(a-c)}/{ac(b-a)(b-c)}

Observe that both numerator and denominators can be expressed as below:

Numerator factors:     a*b*(a-b)(a-c)

Denominator factors:  a*c*(a-b)(-1)*(b-c).

Threfore, the highest common factor(HCF) of Numerator and Denominator =a(a-b).

Therfore, we can divide by the the HCF both numerator and denominator to get the simplified expresion of the given expression:

b(a-c)/{c(-1)(b-c)}, which is equivalent to

b(a-c)/{c(c-b)} or