Respuesta :
The expression [tex]2- \dfrac{x-1}{x+2}[/tex] is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].
We have to find, which equation is equivalent to the given expression.
The given expression is,
[tex]= 2- \dfrac{x-1}{x+2}[/tex]
To determine the equivalent expression following all the steps given below.
- Step1; Taking LCM in the equation,
[tex]\rm = 2-\dfrac{x-1}{x+2}\\\\= \dfrac{2(x+2) - (x-1)}{x+2}\\\\= \dfrac{2x+4-x+1}{x+2}\\\\[/tex]
- Step2; Solving the equation,
[tex]= \dfrac{2x+4-x+1}{x+2}\\\\= \dfrac{x+5}{x+2}\\\\[/tex]
- Step3; rewrite the equation in the small factors,
[tex]=\dfrac{x+5}{x+2}\\\\= \dfrac{x+ 2+3}{x+2}\\\\[/tex]
- Step4; By using partial fraction rewrite the equation,
[tex]= \dfrac{x+2}{x+2} + \dfrac{3}{x+2}\\\\= 1 + \dfrac{3}{x+2}[/tex]
Hence, The expression [tex]2- \dfrac{x-1}{x+2}[/tex] is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].
For more details refer to the link given below.
https://brainly.com/question/2264568
