Answer:
The inequality sign remains same while multiply or divide both sides by positive numbers.
The inequality sign changes while multiply or divide both sides by negative numbers.
Step-by-step explanation:
The given inequality is - 8 < 2.
Now, if we multiply 2 in both sides then - 16 < 4
Again, if we divide by 2 into both sides then - 4 < 1
Therefore, the inequality sign remains the same while multiply or divide both sides by positive numbers.
Now, if we multiply -2 in both sides then 16 > -4
And, if we divide -2 into both sides then 4 > -1
Therefore, the inequality sign changes while multiply or divide both sides by negative numbers. (Answer)
You have the right idea that things need to get multiplied.
What should be done is that the entire fraction needs to get multipled by the lowest common denominator of both denominators.
Let's look at the complex numerator. Its denominators are 5 and x + 6. Nothing is common with these, so both pieces are needed.
The complex denominator has x - 3 as its denominator. With nothing in common between it and the complex numerator, that piece is needed.
So we multiply the entire complex fraction by (5)(x + 6)(x -3).
Numerator:
= (x+6)(x-3) - (5)(5)(x-3)
= (x+6)(x-3) - 25(x-3)
= (x-3)(x + 6 - 25) <--- by group factoring the common x - 3
= (x -3)(x - 19)
Denominator:
Now we put the pieces together.
Our fraction simplies to (x - 3) (x - 19) / 125 (x + 6)