Question

How do you subtract `\frac { 4} { 2r ^ { 4} s ^ { 3} } - \frac { 5} { 9r ^ { 3} s ^ { 3} }`?

Answer 1

`(36-10r)/(18r^4s^3)`

Explanation:

Step 1 is to find the LCD (Least Common Denominator), i.e. the lowest multiple our 2 denominators have in common. The LCD for `2r^4s^3` and `9r^3s^3` is `18r^4s^3`.

Step 2 involves multiplying each fraction by the LCD, and, in doing so, cancelling out any common factors in the numerators and denominators.

In the first fraction, a 2 cancels out of the 18, leaving us with a 9, and the `r^4` and `s^3` in the LCD cancel out completely with the `r^4` and `s^3` in the original denominator, leaving us with only the original 4 in the numerator, times the 9 left in the LCD after cancelling.

In the second fraction, we can cancel an `r^3` out of the `r^4` in the LCD, leaving us with r, and a 9 out of the 18, leaving us with 2r in the LCD, times the 5 in the original numerator, to produce our new numerator 10r.

Step3, as both fractions now have a common denominator, the LCD, we can just subtract the numerators, producing 36 - 10r in the numerator, and the LCD in the denominator, of our final result.