Question

Add or subtract. Simplify your answer.

1. (x^2 + 8x)/ (x - 2)/ (3x + 14)/ (x - 2)

A: ?

2. (2t)/(4t^2) + (2)/(t)

A: ?

3. (m^2 - m - 2)/ (m^2 + 6m +5) - (2)/(m + 5)

A: ?

Answer 1

I suspect #1 is missing parentheses.
If it is a big fraction made up of two small fractions, it would read:
1.((x^2 + 8x)/(x - 2)) / ((3x + 14)/(x - 2))
Remember that parentheses are always there around the numerator and denominator.

These questions are solved using factors.

For number 1, factor as much as possible, and cancel common factors, but be sure to specify that the common factors cannot equal to zero. For example:

1. ((x^2 + 8x)/ (x - 2))÷((3x + 14)/ (x - 2))

= (x(x+8)/(x - 2))÷((3x + 14)/(x-2))
Now multiply the reciprocal of the denominator, instead of ÷
= (x(x+8)/(x-2)) * ((x-2)/(3x+14))
Then the common factor (x-2) can be cancelled <i>if (x-2)≠0, or x≠2</i>.

= x(x+8)/(3x+14) <i> if x≠2 </i>

Attempt the other questions in a similar way.