Fractions and Division

[sportywarbz]

Problem:
((5x-7)/((x-2)(x-1))) divided by ((-1x+4)/((x-2)(x-1)))

then ...
((5x-7)/((x-2)(x-1))) * (((x-2)(x-1))/(-1x+4))
(5x-7)(-1x+4) + (x-2)(x-1)(x-2)(x-1)

Am I right so far?

 

[mmm4444bot]

Problem:
((5x-7)/((x-2)(x-1))) divided by ((-1x+4)/((x-2)(x-1)))

We do not write the coefficient 1 (highlighted in red above).

-1x is written simply as -x


Am I right so far?

Please stand by, while I decipher the meaning of all of those parentheses …

 

[JeffM]

Problem:
((5x-7)/((x-2)(x-1))) divided by ((-1x+4)/((x-2)(x-1))) It really helps to use square brackets and curly brackets rather than parenthesis after parenthesis

then ...
((5x-7)/((x-2)(x-1))) * (((x-2)(x-1))/(-1x+4)) Yes
(5x-7)(-1x+4) + (x-2)(x-1)(x-2)(x-1) Where did the plus come from? In the prior post, we explained how to multiply fractions: (a/b) * (c/d) = (ac)/(bd). Moreover, mmm showed you that after you multiply the numerators and the denominators, you CANCEL like terms in numerator and denominator. CROSS MULTIPLICATION is NOT appropriate

Am I right so far?

 

[mmm4444bot]

((5x-7)/((x-2)(x-1))) * (((x-2)(x-1))/(-1x+4))

You need to recognize common factors in numerators and denominators. Cancelling common factors in fractions make the fractions simplified.

I highlighted two common factors on top and bottom. Cancel them right away. Otherwise, you will work with expressions that are more complicated than need be.

 

[soroban]

Hello, sportywarbz!

\(\displaystyle \frac{5x-7}{(x-2)(x-1)} \div \frac{4-x}{(x-2)(x-1)}\)


\(\displaystyle \text{Then: }\;\frac{5x-7}{(x-2)(x-1)} \cdot \frac{(x-2)(x-1)}{4-x}\)

. . \(\displaystyle =\; (5x-7)(4-x) + (x-2)(x-1)(x-2)(x-1)\;\) . . . . what?

Are you trying to add them?


\(\displaystyle \text{Multiply: }\:\frac{5x-7}{(\rlap{/////}x-2)(\rlap{/////}x-1)}\cdot\frac{(\rlap{/////}x-2)(\rlap{/////}x-1)}{4-x} \;=\;\frac{5x-7}{4-x}\)