Please solve and explain. Photo attached

Question

asked Mar 27, 2021 223k views

1 Answer

Jake Johnson · Answer 1 · 2021-03-31T20:10:42+0000

$((x+1)(x-3))/(x^(2))

Solution:

Given expression:

$((36)/(x^(2))+(36)/(x))/((36)/(x-3))

To solve this expression:

$((36)/(x^(2))+(36)/(x))/((36)/(x-3))

Apply the fraction rule:
$$(a)/((b)/(c))=(a \cdot c)/(b)$

$$=(\left((36)/(x^(2))+(36)/(x)\right)(x-3))/(36)$

Let us solve
(36)/(x^(2))+(36)/(x) .

Least common multiple of
x^(2), x is
x^(2) .

Make the denominator same based on the LCM.

So that multiply and divide the 2nd term by x, we get

$(36)/(x^(2))+(36)/(x)=(36)/(x^(2))+(36 x)/(x^(2))

$=(36+36 x)/(x^(2))

Now, multiply by (x - 3).

$(36+36 x)/(x^(2))(x-3)= ((36 x+36)(x-3))/(x^(2))

$$(\left((36)/(x^(2))+(36)/(x)\right)(x-3))/(36)=(((36 x+36)(x-3))/(x^(2)))/(36)$

Apply the fraction rule:
$((b)/(c))/(a)=(b)/(c \cdot a)$

$$=((36x+36)(x-3))/(x^(2) \cdot 36)$

$$=(36(x+1)(x-3))/(x^(2) \cdot 36)$

Cancel the common factor 36.

$=((x+1)(x-3))/(x^(2))

Hence the solution is
((x+1)(x-3))/(x^(2)) .