Question

Which rational expression has a value of 0 when x = 2 ? A) 7x -5/x2 + 10 B) -3x +6/8x-9 C) -5x + 8 / x-2

Answer 1

answer for this question is (b) - 3 x + 6 x /8x- 9

Answer 2

Answer:

Option: B is the correct answer.

B)     $\dfrac{-3x+6}{8x-9}$

Step-by-step explanation:

We are asked to find the expression which gives the value zero when we substitute x=2.

Hence, we will check each of the options by putting x=2.

A)

$\dfrac{7x-5}{x^2}$

when x=2 we have:

$\dfrac{7\times 2-5}{2^2}\\\\=\dfrac{14-5}{4}\\\\=\dfrac{9}{4}\neq 0$

Hence, option: A is incorrect.

B)

$\dfrac{-3x+6}{8x-9}$

when x=2 we  have:

$=\dfrac{-3\times 2+6}{8\times 2-9}\\\\=\dfrac{-6+6}{16-9}\\\\=\dfrac{0}{7}\\\\=0$

Hence, option: B is correct.

C)

$\dfrac{-5x+8}{x-2}$

when we substitute x=2

we observe that the denominator is zero but the numerator is non-zero.

Hence, x=2 is a excluded point of the rational expression.

Hence, option: C is incorrect.