Question

find the difference quotient of f(x)= (2x)/(x-1)

Answer 1

@Nnesha can you please help me

Answer 2

we need to use formula f(x+h)-f(x) over h right ?

Answer 3

instead of x im using a but yes

Answer 4

f(a)= (2a)/(a-1)

Answer 5

ohh okay so first we have to find f(a+h)
substitute a for a+h

Answer 6

and f(a+h)= (2a+2h)/(-a-h)

Answer 7

am i correct

Answer 8

the denominator would be a-1 = (a+h)-1
so it would be a+h-1 it's not a multiplication

Answer 9

oh alright

Answer 10

alright so now we can substitute f(a+h) for that into the formula \[\huge
\rm \frac{ \frac{ 2a+2h }{ a+h-1 } +\frac{ 2a }{ a-1 } }{ h }\]
now find the common denominator

Answer 11

so you multiply it by h?

Answer 12

first deal with the numerator
2a+2h/a+h-1 + 2a/a-1

Answer 13

what about it

Answer 14

what would be the common denominator ?

Answer 15

brb i'll login to other laptop

Answer 16

shouldnt it be a+h-1?

Answer 17

both denominator are not the same so we should multiply both denominator \[\huge\rm \frac{ (\color{Red}{a-1})(2a+2h) + 2a(\color{blue}{a+h-1}) }{ (a+h-1)(a-1)}\]
and when we find common denominator
we should multiply numerator of first fraction by the denominator of 2nd fraction

Answer 18

and multiply the numerator of 2nd fraction with the denominator of first

Answer 19

so what did get

Answer 20

kinda like cross multiplication