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embizze eNotes educator| Certified Educator

Find the product `(5+3x)/(x-4)*(-4)/(x-4)` :

Like numerical fractions, when multiplying rational expressions we obtain the numerator of the product by multiplying the numerators of the expressions, and the denominator of the product by multiplying the denominators of the expressions.

`(5+3x)/(x-4)*(-4)/(x-4)=((5+3x)(-4))/((x-4)(x-4)) `

`=(-12x-20)/((x-4)^2) `

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`(5+3x)/(x-4)*(-4)/(x-4)=-(12x+20)/((x-4)^2) `

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malkaam | Student

In order to solve the problem, we plot the question in the form of an equation, and therefore we get:

`(5+3x)/(x-4) * -4/(x-4)`

Now we solve the formulated equation by multiplying the two brackets with each other, multiplying each numerical in the bracket with the numerical of the others. And in the denominator, when we multiply to brackets having exactly the same components, the powers of the two brackets are added directly, according to a mathematical rule. 

`[(-4)(5+3x)]/[(x-4)(x-4)]`  

Hence, we get the answer as follows:

`(-20-12x)/[(x-4)^2]`  

sid-sarfraz | Student

(5+3x) / (x-4) . -4 / (x-4)

= (5+3x) . (-4) / (x-4) (x-4)

= -20-12x / (x-4)2

Hence Solved...

maria-vivanco | Student

-32`/ (x-4)^2`

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