Difference Quotient Help!?

Question

here it is

f(x)=(x+5)/(x+3)

find and simplify for [f(x)-f(3)]/(x-3)

please help and show step by step instructions! thank you!

Answer 1

for the f(3) substitute 3 into the equation above and subtract that from (x+5)(x+3)

then divide it by (x-3)


[(x+5)(x+3)-(3+5)(3-3)/(x-3)

[x^2+2x-15-(8)(0)]/(x-3)

[x^2+2x-15]/(x-3)

FACTOR!!

(x+5)(x-3)/(x-3)

=

x+5

Answer 2

f(x) = (x + 5)/(x + 3)
f(3) = (3 + 5)(3 + 3) = 8/6 = 4/3
[f(x) - f(3)]/(x - 3) = [(x + 5)/(x + 3) - 4/3]/(x - 3)
=[3(x + 5) - 4(x + 3)/(3)(x + 3)]/(x - 3)
=[(3x + 15 - 4x - 12)/(3)(x + 3)]/(x - 3)
=[( - x + 3 ) /(3)(x + 3)]/(x - 3)
= -1(x - 3)/(3)(x + 3)(x - 3)
= -1/(3)(x + 3) = -1/(3x + 9)

Answer 3

[f(x) - f(3)] / (x - 3) =
[(x + 5) / (x + 3) - (3 + 5) / (3 + 3)] / (x - 3) =
[(x + 5) / (x + 3) - 8 / 6] / (x - 3) =
[6(x + 5) - 8(x + 3)] / [6(x + 3)(x - 3)] =
(6x + 30 - 8x - 24) / [6(x + 3)(x - 3)] =
(- 2x + 6) / [6(x + 3)(x - 3)] =
- 2(x - 3) / [6(x + 3)(x - 3)] =
- 1 / (3x + 9)

Answer 4

f(x)=(x+5)/(x+3)......equation 1

let [f(x)-f(3)]/(x-3)]=0
cross multiplying it v get
f(x)-f(3)=0
f(x)=f(3) ........[taking f(3) to right]
therefore x=3...equation 2

now taking equation 1 we have
f(x)=(x+5)/(x+3)
f(3)=(3+5)/(3+3)......substituting for x from equation 2
=(8)/(6)
=4/3
=1.33

therefore ....f(x)=4/3 or 1.33

Answer 5

to first find f(3)
just substuite the value of 3 in place of x

f(3) = 3+5/3+3
f(3)= 4/3
[f(x)-f(3)]/(x-3) = x+5/x+3 - 4/3
. ----------------------.
. x-3

(x+5)3 -4(x+3)
.---------------------
. 3(x+3)(x-3)

3x+15 -4x-12
.-----------------
. 3(x+3)(x-3)


-(x -3)
.---------
. 3(x+3)(x-3)

= -1
.--------
. 3(x +3)

Answer 6

shouldn't you be doing your OWN homework?