Respuesta :
Answer:
[tex]-\frac{h}{x(x+h)}[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=\frac{1}{x}[/tex]
To find [tex]f(x+h)-f(x)[/tex]
Solution.
We will first find [tex]f(x+h)[/tex] by plugging in [tex](x+h)[/tex] in place of [tex]x[/tex] in [tex]f(x+h)[/tex]
∴ [tex]f(x+h)=\frac{1}{x+h}[/tex]
So, [tex]f(x+h)-f(x)[/tex]
⇒ [tex]\frac{1}{x+h}-\frac{1}{x}[/tex]
Taking LCD as product of denominators as they are unknown variables.
Making the denominators common by multiplying the with corresponding terms.
⇒ [tex]\frac{1\times x}{(x)(x+h)}-\frac{1\times (x+h)}{(x)(x+h)}[/tex]
⇒ [tex]\frac{x}{(x)(x+h)}-\frac{x+h}{(x)(x+h)}[/tex]
⇒ [tex]\frac{x-(x+h)}{(x)(x+h)}[/tex] [Subtracting the numerators]
⇒ [tex]\frac{x-x-h}{(x)(x+h)}[/tex]
⇒ [tex]\frac{-h}{(x)(x+h)}[/tex]
⇒ [tex]-\frac{h}{x(x+h)}[/tex] (Answer)
