Help please with this question

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asked Jul 20, 2021 150k views

1 Answer

Thankyoussd · Answer 1 · 2021-07-24T18:31:42+0000

Given:

The given two functions are
f(x)=(4 x^(2)+24 x)/(x^(2)-11 x+30) and
g(x)=(x-5)/(x^(2))

We need to determine the value of R(x)

Value of R(x):

The value of R(x) can be determined by R(x) = f(x) × g(x)

Substituting the values, we get;

$R(x)=(4 x^(2)+24 x)/(x^(2)-11 x+30) \cdot (x-5)/(x^(2))$

Multiplying the fractions, we have;

$R(x)=(\left(4 x^(2)+24 x\right)(x-5))/(\left(x^(2)-11 x+30\right) x^(2))$

Let us factor out the common term 4x from the term (4x² + 24x)

Thus, we have;

$R(x)=(4 x(x+6)(x-5))/(\left(x^(2)-11 x+30\right) x^(2))$

Let us factor the term (x² -11x + 30), we get;

R(x)=(4(x+6)(x-5))/(x(x-5)(x-6))

Cancelling the common term, we have;

R(x)=(4(x+6))/(x(x-6))

Thus, the value of R(x) is
(4(x+6))/(x(x-6))