Question

Reduce To Simplest Form.

8/6 + (-9/5) =​

Answer 1

`(8)/(6) +(-9)/(5)` =
`(-7)/(15)`

Explanation:

To add these two fraccions we need them to have the same denominator. In order to do so, we calculate the least common multiple (LCM) by factorizing the original denominators, selecting both common (raised to the highest power) and not common factors.

6 =
`2*3`; 5 = 5

LCM (3, 5) =
`2*3*5 = 30`

Now we rewrite the two fractions with their new denominator (30) and we find the numerator by dividing the new denominator with the old one and multiplying that result by the old numerator. Thus:

• To calculate the numerator of the 1st fraction ->
  `(30/6)*8 = 40`

• To calculate the numerator of the 2nd fraction ->
  `(30/5)*(-9) = -54`

Getting this:
`(40)/(30) +(-54)/(30)` =
`(-14)/(30)`

Now we simplify the fraction by dividing it by 2 (we can also calculate the GCD [Greatest common divisor] {which is calculated by choosing only the common factors (unlike the LCM}). Thus:

• Simplifying the numerator:
  `-14 / 2 = -7`

• Simplifying the denominator [text]30/2 = 15[/tex]

Now we have the simplest form:
`(-7)/(15)`

I hope this was helpful.

Answer 2

Explanation:

8/6 + (- 9/5) =

8/6 - 9/5 =

40/30 - 54/30 =

-14/30 reduces to - 7/15 <==