Rowan Huynh

2022-04-26

Simplifying this algebraic fraction

I don't understand how to simplify this fraction:

$\frac{12ab-12b}{8ac-24c}$

This is my idea to what should be done, but I think it is totally wrong:

$\frac{12ab-12b}{8ac-24c}=\frac{12\cdot a\cdot b-12\cdot b}{8\cdot a\cdot c-24\cdot c}=\frac{12{b}^{2}-12b}{8c-24c}=\frac{b}{8c-24c}=?$

Edit: I want to simplify the fraction.

I don't understand how to simplify this fraction:

This is my idea to what should be done, but I think it is totally wrong:

Edit: I want to simplify the fraction.

otposlati9u8

Beginner2022-04-27Added 19 answers

In general

$\frac{12ab-12b}{8ac-24c}\ne \frac{12{b}^{2}-12b}{8c-24c}.$

You can divide $}^{1$ both numerator and denominator by $4=gcd(12,8,24)$

$\frac{12ab-12b}{8ac-24c}=\frac{\left(\frac{12}{4}\right)ab-\left(\frac{12}{4}\right)b}{\left(\frac{8}{4}\right)ac-\left(\frac{24}{4}\right)c}=\frac{3ab-3b}{2ac-6c}.$

If you want you can factor the numerator and denominator

$\frac{3ab-3b}{2ac-6c}=\frac{3b(a-1)}{2c(a-3)}.$

In greater detail:

$\frac{12ab-12b}{8ac-24c}=\frac{\frac{12ab-12b}{4}}{\frac{8ac-24c}{4}}=\frac{\frac{12ab}{4}-\frac{12b}{4}}{\frac{8ac}{4}-\frac{24c}{4}}=\frac{\frac{12}{4}ab-\frac{12}{4}b}{\frac{8}{4}ac-\frac{24}{4}c}=\frac{3ab-3b}{2ac-6c}$.

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