VERY VERY Tricky Problem, I cannot solve this?!?!?

Question

Simplify this expression: (dividing fractions)
s^3/t^2 ÷ (s + t)/(s - t)

Nope, it is dividing one fraction by another fraction, all filled with variables.

Answer 1

First, note that (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad)/(bc). So applying this to the fractions:

(s³/t²) ÷ ((s + t)/(s - t))
(s³(s - t))/(t²(s + t))
(s⁴ - s³t)/(st² + t³)

Note that no factors cancel, so this is the simplest possible form. However, there is an interesting decomposition we can perform:

(s³(s - t))/(t²(s + t))
(s³(s + t))/(t²(s + t)) - 2ts³/(t²(s + t))
s³/t² - 2s³/(st + t²)

However, your teacher is probably looking for the first answer, namely (s⁴ - s³t)/(st² + t³).

Answer 2

This problem is already solved because there is no like factors to cancel out.

The rule for this problem is divide in order from left to right.

s^3
_____________
t^2 (s+t)(s-t)

The slash and division sign can make things complication if the correct parenthesis is not in place to show the order of operations. For example if brackets were meant [(s+t)(s-t)] then you would invert the denominator and multiply it by the top or right fraction. Other wise you have to follow order of operation. do division from left to right.

Hoped this helped.

Answer 3

the t's would cancel out because ones a neg. and ones positive
s^3/t^2 ÷ s/s

s/s would equal one

then cross multiply by the reciperical of s/s which would just be s/s

s^3/t^2 * 1

and it would be s^3/t^2 because anything times one is itself

but im not 100% on that

Answer 4

you need to recognise the DOMINANT DIVISION since division is non-commutative i.e.
a /b does not equal b / a unlike multiplication a*b = b*a

with DOMINANT DIVISION use inverse multiplication e.g
a/b ÷ c/d = a / b * d / c
NOTE ÷ c/d becomes * d / c

Try your expression now replacing a, b, c, d and see how you get on

Answer 5

I think there needs to be an "=" sign between these instead of a division sign, therefore solving to s and t.

Answer 6

[s^3 / t^2] / [(s + t) / (s -- t)]
= s^3*(s -- t) / t^2*(s + t)
= (s^4 -- s^3*t) / (st^2 + t^3)

Answer 7

s^3/t^2 * (s - t)/(s + t)

s^3(s - t)/t^2(s + t) this is how far it goes if sign between () was similar than we can cancel it but its not so thats all

Answer 8

s^3/t^2 ÷ (s + t)/(s - t)

cannot decide where (s-t) belongs (numerator or denominator) aborting answer

and in one place we have ÷
and another place we have /

that suggests an errror

Answer 9

5^3? 7+5 or 7x=8Y

Answer 10

s^3 / t^2 ÷ (s + t) / (s - t)
(s^3) * (s-t) ÷ (s + t) * t^2
(s^4 -ts^3) ÷ (st^2 + t^3)