Question

What is the sum of the rational expressions below?

2x-1
7x+x=2
X-2
OA. 9x²-5x+2
7x²-2
OB. 9x²-5x+2
7x²-14x
O C.
O D.
2x²-5x+2
7x²-14x
3x-1
8x-2

Answer 1

C

Explanation:

To find the sum of the rational expressions, we need to add the two expressions and simplify if possible:

(2x-1)/(7x+x+2) + (x-2)/(8x-2)

Simplifying the denominators, we get:

(2x-1)/(8x+2) + (x-2)/(8x-2)

Now, we need to find the LCD, which is (8x+2)(8x-2) = 64x²-4:

[(2x-1)(8x-2) + (x-2)(8x+2)] / (64x²-4)

Simplifying the numerator, we get:

[16x²-4x-16x+4+8x²-2x+16x-4] / (64x²-4)

Combining like terms, we get:

(24x²-2) / (64x²-4)

Factoring out a 2 from the numerator and denominator, we get:

2(12x²-1) / 2(32x²-2)

Simplifying further, we get:

(12x²-1) / (16x²-1)

Therefore, the sum of the rational expressions is:

12x²-1

-----------

16x²-1

So, the answer is option C.