Answer:
Option: B is the correct answer.
B) [tex]\dfrac{-3x+6}{8x-9}[/tex]
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)
[tex]\dfrac{7x-5}{x^2}[/tex]
when x=2 we have:
[tex]\dfrac{7\times 2-5}{2^2}\\\\=\dfrac{14-5}{4}\\\\=\dfrac{9}{4}\neq 0[/tex]
Hence, option: A is incorrect.
B)
[tex]\dfrac{-3x+6}{8x-9}[/tex]
when x=2 we have:
[tex]=\dfrac{-3\times 2+6}{8\times 2-9}\\\\=\dfrac{-6+6}{16-9}\\\\=\dfrac{0}{7}\\\\=0[/tex]
Hence, option: B is correct.
C)
[tex]\dfrac{-5x+8}{x-2}[/tex]
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.
