Describe the error made in subtracting the two rational expressions shown:

[tex]\begin{array}{l}
\frac{1}{x-2}-\frac{1}{x+1} \
=\frac{x+1}{(x-2)(x+1)}-\frac{x-2}{(x-2)(x+1)} \
=\frac{-1}{(x-2)(x+1)}
\end{array}[/tex]

First.
Calculate f'(x) = (2x/x-1)' = (-2)/ ( x − 1 ) 2 ; when x is not 1;
Second.
Calculate f'(0) = -2 => the difference quotient (f(a+h)-f(a))/ h, where hod want equal 0 is -2;
Third.
f(a) = 2a/a-1; f(a+h) = (2a+2h)/(a+h-1);

Answered by crisforp | 2024-06-10

1 ;

Answered by titir15 | 2024-06-12

To find f ( a ) , use f ( a ) = a − 1 2 a ​ . For f ( a + h ) , use f ( a + h ) = a + h − 1 2 ( a + h ) ​ . The difference quotient is given by ( a + h − 1 ) ( a − 1 ) 2 ( ah − a + h ) ​ .
;

Answered by crisforp | 2024-12-04