solve the following for x. x/6 - x/8 = 1 I have this one too. x/x-2 - x+1/x=8/x^2-2x?

Question

I am having trouble factoring them first. Could anyone please help and show the steps to get the answer. I need to see the steps so I can do the rest of the problems like these two.

Answer 1

1.4x-3x/24=1
x=24
2.[x^2-(x+1)(x-2]/x(x-2)
=8/x(x-2)
(x^2-x^2+x+2)=8
x=6

Answer 2

1.) x/6 - x/8 = 1

Step 1: Either find the common denominator, or simply multiply by the opposing fracton's denominator:
x/6 * 8/8 - x/8 * 6/6 = 1

Step 2: Combine the like terms
8x/48 - 6x/48 = 1
2x/48 = 1

Step 3: Simplify and solve:
x/24 = 1
x = 24

2.) x/x-2 - x+1/x=8/x^2-2x?

Step 1: Express the equation so that it equals 0.
x/x-2 - x+1/x - 8/x^2 + 2x = 0

Step 2: Find a common denominator:
In this case, the simplest method is to use (x-2) * x^2.
x/x-2 * x^2/x^2 - x+1/x * (x-2)(x)/(x-2)(x) - 8/x^2 * (x-2)/(x/2) + 2x * (x-2)(x^2)/(x-2)(x^2)= 0

Step 3: Combine like terms:
(x * x^2 - (x+1)(x-2)(x) - 8(x-2) + 2(x)(x-2)(x^2)) / (x-2)(x^2) = 0
(x^3 - x^3 + x^2 + 2x - 8x + 16 + 2x^4 - 4x^3) / (x-2)(x^2)
(2x^4 - 4x^3 +x^2 - 6x + 16) / (x-2)(x^2) = 0

Step 4: Multiply both sides by (x-2)(x^2).
2x^4 - 4x^3 + x^2 - 6x + 16 = 0

And then factor...

Answer 3

OK!
ques 1:
for this ques, u must first multiply both fractions with their LCM (least comon multiple)
LCM = 24
x/6 - x/8 =1
(4x-3x)/24 = 1
4x-3x = 24*1 (*=multiply)
x=24

ques 2:
this question is a bit tricky because the LCM involves algebra
x/x-2 - x+1/x = 8/x^2 - 2x
but just the same though, get their LCM

I'm not quite sure though your 2nd part of the equation,is it x plus (1 over x) or (x+1) over x??
So, confirm the question and I'll solve for you again :)
Good Luck!

Answer 4

x/6-x/8=1

first you simplify the equation so there aren't any fractions. find the first number that can be divided by 6 and 8. that is 24. then multiply each section by 24/1.

(24/1)(x/6)-(24/1(X/8)=(24/1)(1)
24x/6-24x/8=24
4x-3x=24
1x=24
x=24

Try to look at a algebra textbook to find the proper terms. I'm pretty sure my answer is correct but I don't how to explain it very well.