Question

(3)/(x+4)=3 + 4(x-2)

Answer 1

carry out distributive property on that right side first... can you simplify the right side?

Answer 2

oops i typed the problem wrong.
(3)/(x+4)=3+4/(x-2)

Answer 3

lol....
ok then... what we need to do here is to clear the fractions by multiplying BOTH SIDES by (x+4)(x-2)...

Answer 4

\(\large \frac{3}{x+4}=3+\frac{4}{x-2} \)
\(\large \color {red} {(x+4)(x-2)}[\frac{3}{x+4}]=\color {red} {(x+4)(x-2)}[3+\frac{4}{x-2}] \)

can you simplify the left/right sides?

Answer 5

i dont understand. can you show me how it looks further

Answer 6

ok.... let's work with that left side first....
notice the (x+4) will cancell:

\(\large \cancel{(x+4)}(x-2)[\frac{3}{\cancel{x+4}}]=3(x-2) \)
you follow? this is only the left side...

Answer 7

i follow!

Answer 8

great... :) now let's work on the right side...

Answer 9

the right side is: \(\large (x+4)(x-2)[3+\frac{4}{x-2}] \)

from here carry out distributive property to get:
\(\large 3(x+4)(x-2)+(x+4)(x-2)\frac{4}{x-2} \)

notice the (x-2) will cancel:
\(\large 3(x+4)(x-2)+(x+4)\cancel{(x-2)}\frac{4}{\cancel{x-2}} \)

can u simplify this?

Answer 10

is this ok so far?

Answer 11

i dont know how to simplify that

Answer 12

i'll help... but do you follow the algebra up to that point?

Answer 13

yes i do

Answer 14

ok.... from that last step,

\(\large 3(x+4)(x-2)+(x+4)\cancel{(x-2)}\frac{4}{\cancel{x-2}} \)
= \(\large 3(x+4)(x-2)+4(x+4) \)
= \(\large 3(x^2+2x-8)+4x+16 \)
= \(\large 3x^2+6x-24+4x+16 \)
= \(\large 3x^2+10x-8 \)

remember, this is only the right side... you understand up to this point?

Answer 15

yes

Answer 16

ok.... now we cleared the fractions to come up with an equivalent equation to the original. we have the left side = the right side:

\(\large 3(x-2)=3x^2+10x-8 \)

can you solve from here?

Answer 17

this is a quadratic equation so solve this like any quadratic by completing the square, factoring, quadratic formula....

Answer 18

yea thanks!