Question

I am trying to figure out how to solve this proportion, 4x^2/ 8x^2 - 8x = 2/x, I am stuck, I got an answer, but I checked it and it was wrong. Does anyone know how to do it? If so, can u please show me the work?

Answer 1

Solving for x

Answer 2

\[ \frac{4x^2}{8x^2 -8x} =\frac{2}{x} \]

can you factor 8x from the denominator of the fraction on the left side ?

Answer 3

Yes

Answer 4

what do you get ?

Answer 5

Don't u first have to simplify the proportion?

Answer 6

what do you get when you factor 8x from the denominator ?

Answer 7

this is the first step in simplifying the left side

Answer 8

I got x/-16x

Answer 9

factor out 8x from
\[ 8x^2 -8x \]
what do you get ?

Answer 10

notice both terms can be evenly divided by 8x

Answer 11

0?

Answer 12

do you know the distributive property:
8x( x -1)
what do you get if you multiply the 8x times each term inside the parens ?

Answer 13

8x^2 + 8x?

Answer 14

yes. except it is 8x^2 -8x (with a minus sign)

notice that 8x^2 - 8x can be written
8*x*x - 8*x
notice that there is an 8*x in both terms, so you can "undo" the distributive property
you get 8*x * ( x - 1)

you now have
\[ \frac{4x^2}{8x(x-1)} = \frac{2}{x} \]

notice that you can simplify the left. what is 4/8 ?

Answer 15

1/2

Answer 16

what is x^2/x or x*x/x ?

Answer 17

X

Answer 18

that means you now have
\\[ \frac{\cancel{4x^2}x}{\cancel{8x}2(x-1)} = \frac{2}{x} \\ \frac{x}{2(x-1)} =\frac{2}{x}\]

do you know how to cross multiply?

Answer 19

Yes

Answer 20

what do you get ?

Answer 21

\frac{\cancel{4x^2}x}{\cancel{8x}2(x-1)} = \frac{2}{x} \\ \frac{x}{2(x-1)} =\frac{2}{x}\], I don't get what this means

Answer 22

I was trying to show that the 4x^2/8x simplifies to 1x/2 or just x/2

Answer 23

I got 4 = x^2

Answer 24

X^2 - 4

Answer 25

if you do it step by step
\[ \frac{4x^2}{8x} = \frac{1 x^2}{2x} \]
using 4/8= 1/2
and then
\[ \frac{1 x^2}{2x} = \frac{1 x}{2} = \frac{x}{2}\]
using x^2/x = x

Answer 26

X = 2, x = -2?

Answer 27

can you show how you did the cross multiply?

Answer 28

i cross multiplied x/2 and 2/x and got x^2 = 4

Answer 29

that is correct, except that your problem is
\[ \frac{x}{2(x-1)} =\frac{2}{x} \]

Answer 30

I got 8x + 8 = x^2

Answer 31

show your steps

Answer 32

I multiplied 2x + 2 by 2 and get 4x + 4?

Answer 33

ok, but there is no 2x+2 Do you mean 2(x-1) = 2x - 2 ?

Answer 34

Yea

Answer 35

4x -4

Answer 36

what do you get when you cross multiply
\[ \frac{x}{2(x-1)} =\frac{2}{x} \]

Answer 37

4x - 4 = x^ 2

Answer 38

ok, now move all the terms to the x^2 side.
add -4x to both sides
add +4 to both sides
what do you get ?

Answer 39

So, x = 2?

Answer 40

are you a human calculator? we have to solve a quadratic equation here.
4x - 4 = x^ 2

the first step is put it in standard form.
add -4x to both sides
add +4 to both sides
what do you get ?

Answer 41

x^2 - 4x + 4

Answer 42

what happened to the = sign and the other side ?

Answer 43

you should get
x^2 - 4x + 4 = 0

now you have to factor this. Can you do that ?

Answer 44

Yes, I got x = 2 and x = 2

Answer 45

to show your work:
x^2 - 4x + 4 = 0
(x-2)(x-2) =0
so either (x-2)=0 or (x-2)=0 (we get "repeated" roots)
x-2=0
x= 2 (twice)

Answer 46

Okay, thanks a bunch!