How do I solve this?

Mathematics

1 answer:

nikitadnepr [17]4 years ago

4 0

The answer will be B. Hope it help!

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Factor out the coefficient of the variable 5/6s+2/3

DochEvi [55]

Okay. so I'm gonna assume you know what factor out means--were gonna take out 5/6. what we need to know is, how does that affect our ending number 2/3? well, we're gonna have 5/6 times some stuff first off, right?

5/6 ( )

so what's in the parenthesis? well, if we distribute in our mind, S would just have to be by itself for it to work out. so we have

5/6 ( s )

but what about 2/3? well, if we're multiplying everything on the inside by 5/6, how can be get it to cancel and leave 2/3 alone? we could divide 2/3 by 5/6, right?

5/6 ( s + (2/3) / (5/6) )

now, when we distribute our 5/6, we'll have just 2/3 at the end. now let's simplify that end term so it looks a little better. if we divide by a fracion, that's the same as multiplying by the flipped version, so let's do that.

2/3 / 5/6 = 2/3 × 6/5 = 2 (6) / 5 (3) = 12/15

we can reduce 12/15 by dividing the top and bottom by three.

= 4/5

so our final answer would be:

5/6 [S + 4/5] you can redistribute to make sure it matches. Anyway, hope that helps!

6 0

3 years ago

Divide.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

yulyashka [42]

It's not clear whether the problem is to:

(1) divide $x^2-4$ by $\dfrac{x-8}{x-2}$ , or

(2) divide $\dfrac{x^2-4}{x-8}$ by $x-2$ .

But with only two possible cases, that's not much work to do.

$\drac{x^2-4}{\frac{x-8}{x-2}}=\dfrac{(x^2-4)(x-2)}{x-8}=\dfrac{x^3-2x^2-4x+8}{x-8}$

Synthetic division yields a quotient and remainder of $x^2+6x+44+\dfrac{360}{x-8}$ (see attachment for how the algorithm was carried out).

In the other case,

$\dfrac{\frac{x^2-4}{x-2}}{x-8}=\dfrac{\frac{(x-2)(x+2)}{x-2}}{x-8}=\dfrac{x+2}{x-8}$

provided that $x\neq2$ . Synthetic division can be used again here, but this is quite easy to deal with by just doing some easy manipulation of the numerator:

$\dfrac{x+2}{x-8}=\dfrac{x-8+10}{x-8}=\dfrac{x-8}{x-8}+\dfrac{10}{x-8}=1+\dfrac{10}{x-8}$

(also provided that $x\neq 8$ )