Having difficulty with some Algebraic problems, For instance 2x-7/2x+4 = 2/3 and 1/x - 2/2x+1 = 1/2x^2+x.?

Question

Not looking for just Answers but help. I am not trying to gain answers because I am lazy but could actually use some assistance in solving these. Thanks in advance

Answer 1

Problem 1

2x-7/2x+4=2/3
Set it up like a proportion

_2x-7 _ = _2_
2x+4 3

Cross multiply (2x-7)3 = 2(2x+4)
Solve it 6x-21 = 4x + 8
Subtract 4x from both sides 2x-21 = 8
Add 21 2x = 29
Divide 2 x = 29/2

Answer 2

OK. Lets consider your equation 2x-7/2x+4=2/3. First of all you have to take all x terms to one side of the equations and the values to the other side. Now your equation becomes 2x-7/2x=2/3-4. Then you can write this as (2-7/2)x=2/3-12/3. Now you get -3/2x=-10/3. When you multiply both sides of the equation by -1 you get 3/2x=10/3. So the value for x is equal to 10/3*2/3 (by multiplying both sides by 2/3). Then the answer is 20/9=2.22

Answer 3

(2x-7)/(2x+4)=2/3 clear it of fractions by multiplying by the common denominator
3(2x-7=2(2x+4)
6x-21=4x+8
2x=29
x=29/2

same process
2x+1-2x=1
1=1
This implies that any real number except 0 and -1/2 will be true. Try it
1/9 - 2/(2*9+1) = 1/(2*9²+9)
1/9-2/19 = 1/171
(19-18)/9*19=
1/171=1/171

Answer 4

Multiply by the denominators - so you have no fractions and no x underneath.

Then simplify - you should get solvable quadratic equations.