Answer:
1).
2).
Step-by-step explanation:
In this question we have to write the fractions in the factored form.
Rational expressions are and
.
1).
Factored form of the denominator (x² - x - 12) = x² - 4x + 3x - 12
= x(x - 4) + 3(x - 4)
= (x + 3)(x - 4)
Therefore.
2).
Factored form of the denominator (x² - 16) = (x - 4)(x + 4)
[Since (a²- b²) = (a - b)(a + b)]
Therefore,
s = hours it takes the small pipe on its own.
L = hours it takes the large pipe on its own.
we know the small pipe can do it in 11 hours total, so s = 11, so, how much of the whole job has the small done in 1 hour only?
well, if it takes 11 hours to do the whole thing, in 1 hour it has done only 1/11 of the whole job.
we know both pipes working together can do it in 6 hours flat. So in 1 hour only, both of them have done only 1/6 of the whole thing.
in that 1 hour, how much has the large one done? well, it has only done 1/L of the job.
and you can round that up as needed.
