Question

Simplify quantity 1 over 36 minus 1 over x squared all over 1 over 6 plus 1 over x.

Answer 1

Can you put into the equation format?

Answer 2

Is this it?

\( \dfrac{ \dfrac{1}{36} - \dfrac{1}{x^2} } {\dfrac{1}{6} + \dfrac{1}{x}}\)

Answer 3

Yes

Answer 4

Step 1: Find the LCD of every small denominator: 36, x^2, 6, and x.
Do that. What do you get?

Answer 5

36x

Answer 6

6x?

Answer 7

The 36 is correct, but since you have x^2 and x, the LCD is 36x^2.

Answer 8

Ok so far?

Answer 9

Step 2: Multiply the numerator and denominator of the main fraction by the LCD you just found in Step 1.

Answer 10

\( =\dfrac{36x^2}{36x^2} \times \dfrac{ \dfrac{1}{36} - \dfrac{1}{x^2} } {\dfrac{1}{6} + \dfrac{1}{x}}\)

Answer 11

When you multiply fractions together, you multiply the numerators and yo9u multiply the denominators.

\( =\dfrac{ 36x^2 \left(\dfrac{1}{36} - \dfrac{1}{x^2}\right) } {36x^2 \left(\dfrac{1}{6} + \dfrac{1}{x} \right)}\)

Answer 12

Now you use the distributive property in the numerator and in the denominator.

\( =\dfrac{ 36x^2 \times \dfrac{1}{36} - 36x^2 \times\dfrac{1}{x^2} } {36x^2 \times \dfrac{1}{6} + 36x^2 \times\dfrac{1}{x} }\)

Now all small denominators cancel out.

\( =\dfrac{ \cancel{36}x^2 \times \dfrac{1}{\cancel{36}} - 36\cancel{x^2} \times\dfrac{1}{\cancel{x^2}} } {\cancel{36} 6 x^2 \times \dfrac{1}{\cancel{6}} + 36\cancel{x^2}x \times\dfrac{1}{\cancel{x}} }\)

After all this you get you get:

\(=\dfrac{x^2 -36}{6x^2 + 36x} \)

Now we factor the numerator and denominator:

\(=\dfrac{(x + 6)(x - 6)}{6x(x + 6)} \)

Finally we reduce this fraction to get:

\(=\dfrac{\cancel{(x + 6)}(x - 6)}{6x\cancel{(x + 6)}} \)

\(\dfrac{x - 6}{6x} \)