x/(2x-4)-7=1/(x-2)..
How I clear this denominator if I must clear it at all.. Im not sure how to approach these problems.I have several others similar to this
1/2y+ 4= 1/7y
I changed the denominators to 14y, then got 7/14y+ 4= 2/7y but my online homework says that is incorrect.
5/8x + 2/7 = -2/7x+ 3/8
and also 3/(x-4)=7/(x-8)..PLEASE HELP ME PLEASEEEEEEEEEE, I have been stuck for hours a just don't know how to approach these problems
The common denominator is 2(x-2). If you multiply through by that, you get
x - 7*2(x-2) = 1*2
Now just proceed normally:
x - 14x + 28 = 2
-13x = -26
x = 2
For the next one, you must be interpreting the equation as
1/(2y) + 4 = 1/(7y)
if you multiply by 14y, you get
y + 4*14y = 2
y+56y = 2
y = 2/57
If, as I suspect, the equation is really
(1/2)y + 4 = (1/7)y, then you just have a LCD of 14, not 14y. Clear that and you get
7y + 4*14 = 2y
-5y = 56
y = -56/5
I see no advantage in either interpretation, except for choosing the right one!
(5/8)x + 2/7 = (-2/7)x + 3/8
With a LCD of 56, you get
35x + 2*8 = -16x + 21
51x = 5
x = 5/51
Your last one
3/(x-4)=7/(x-8)
is the easiest of the three equations
just multiply each side by (x-4)(x-8) , which is sometimes called "cross-multiplying"
7(x-4) = 3(x-8)
7x - 28 = 3x - 24
4x = 4
x = 1
To solve equations with fractions, you need to clear the denominators. Here's the step-by-step process to approach these problems:
Problem 1: x/(2x-4) - 7 = 1/(x-2)
To clear the denominators, you need to multiply every term by the least common denominator (LCD) of (2x-4) and (x-2), which is (2x-4)(x-2).
1. Start by multiplying both sides of the equation by (2x-4)(x-2):
(x/(2x-4) - 7)(2x-4)(x-2) = (1/(x-2))(2x-4)(x-2)
2. Distribute:
(x(x-2) - 7(2x-4))(x-2) = (1(x-2))(2x-4)(x-2)
2. Simplify:
(x^2 - 2x - 14x + 28)(x-2) = (2x-4)(x-2)
(x^2 - 16x + 28)(x-2) = (2x-4)(x-2)
3. Expand:
x^3 - 2x^2 - 16x^2 + 32x + 28x - 56 = 2x^2 - 4x - 4x + 8
4. Simplify and rearrange:
x^3 - 18x^2 + 60x - 56 = 2x^2 - 8x + 8
x^3 - 20x^2 + 68x - 64 = 0
This equation can be solved further through factoring, the quadratic formula, or other methods.
Problem 2: 1/(2y) + 4 = 1/(7y)
To clear the denominators, you need to multiply every term by the LCD of 2y and 7y, which is 14y.
1. Begin by multiplying both sides of the equation by 14y:
(1/(2y) + 4) * 14y = (1/(7y)) * 14y
2. Simplify:
7 + 56y = 2
3. Rearrange terms:
56y = 2 - 7
56y = -5
y = -5/56
Problem 3: 5/(8x) + 2/7 = -2/(7x) + 3/8
To clear the denominators, you need to multiply every term by the LCD of 8x and 7x, which is 56x.
1. Multiply both sides of the equation by 56x:
(5/(8x) + 2/7)(56x) = (-2/(7x) + 3/8)(56x)
2. Simplify:
35 + 16x = -16 + 21x
3. Rearrange terms:
16x - 21x = -16 - 35
-5x = -51
x = 51/5
Problem 4: 3/(x-4) = 7/(x-8)
To clear the denominators, you need to multiply every term by the LCD of (x-4) and (x-8), which is (x-4)(x-8).
1. Multiply both sides of the equation by (x-4)(x-8):
(3/(x-4))(x-4)(x-8) = (7/(x-8))(x-4)(x-8)
2. Simplify:
3(x-8) = 7(x-4)
3x - 24 = 7x - 28
3x - 7x = -28 + 24
-4x = -4
x = 1
Now you have successfully solved all the given equations.