Multiply or divide

Question

5) 3/x-2 times x^2-2/12

 

6)5x/x^2+2x divided by 30x^2/x+2

Answer 1

5)

 

[3 / (x - 2)] * [(x² - 2) / 12]

 

 

When we multiply rational expressions, it is like multiplying fractions.  We simply multiply the numerators over multiply the denominators.

 

[3 * (x² - 2)] / [(x - 2) * 12]

 

Since 3/12 = 1/4, we will have

 

 

(x² - 2) / (4(x - 2))

 

We can no longer simplify.

 

 

6) 

 

[5x / (x² + 2x)] / [30x² / (x + 2)]

 

 

When we divide, we multiply by the reciprocal of the second rational expression.  This is just like dividing fractions.

 

[5x / (x² + 2x)] * [(x + 2) / 30x²]

 

 

Since 5x / 30x² = 1/(6x), we obtain

 

(x + 2) / (6x(x² + 2x)) =

 

(x + 2) / (6x*x(x + 2)) =

 

(x + 2) / (6x²(x + 2)) =

 

1 / (6x²)