which method for solving 6x + 7/ 2x+1 - 6x+1/2x = 1

[Kristen_Opp]

the instructions for this set of problems is to solve by any method... and I'm getting a little confused.

1. 6x + 7/ 2x+1 - 6x+1/2x = 1

I tried to multiply both sides by (2x+1) and (2x) but seem to be doing something wrong. the answer is 1/2 and I have no idea how they got it.

2. this one has me confused only because we haven't addressed any questions in this chapter using square root signs. I don' know how to simplify it in order to solve it using one of the quadratic methods.

square root of X - the square root of 2x+1+1 =o
there are several problems like this one and I just don't know where to start. should I times the whole problem to the power of two to remove the square roots?
Thanks in advance! : )

 

[Unco]

Re: which method? : )

the instructions for this set of problems is to solve by any method... and I'm getting a little confused.

1. (6x + 7)/(2x+1) - (6x + 1)/(2x) = 1

(Note the uses of parentheses.)

I tried to multiply both sides by (2x+1) and (2x) but seem to be doing something wrong. the answer is 1/2 and I have no idea how they got it.
You have the right idea, Kristen. Show us your effort.

2. this one has me confused only because we haven't addressed any questions in this chapter using square root signs. I don' know how to simplify it in order to solve it using one of the quadratic methods.

square root of X - the square root of 2x+1+1 =o
there are several problems like this one and I just don't know where to start. should I times the whole problem to the power of two to remove the square roots?

The "power of two" is not a number, so we say to "raise both sides by the power of two" (or "square both sides") as opposed to "times".

If you mean: sqrt(x) - sqrt(2x + 1) + 1 = 0, then rearrange:

sqrt(x) + 1 = sqrt(2x + 1)

And square both sides, as you suggested, and simplify. Another squaring of both sides will be necessary to get rid of the remaining square root. See how you go and show your work.

Thanks in advance! : )