Question

how do can i add (2x)/(3x-5) to (x+1)/2x.. use complete sentence to explain your answer.

Answer 1

Just to be clear your question is:
\[\frac{2x}{3x-5}+ \frac{x+1}{2x}\]
Right?

Answer 2

yes @AskingTheHardQuestion

Answer 3

\[\frac{2x}{3x-5}+ \frac{x+1}{2x} \implies \frac{(7x + 5) (x-1)}{2x(3x-5)}\]
Step 1: Put fractions over a common denominator: 2x(3x-5).

Answer 4

Step 2: Use FOIL:
\[2x \times 2x(3x-5) \implies 12x-10x \implies 2x\]
So far we have: \[\frac{2x}{3x-5}+\frac{x+1}{2x}\]

Answer 5

Step three:
\[\frac{x+1}{2 x} = \frac{4 x^2}{2 x (3 x-5)}+\frac{(x+1)(3 x-5)}{2 x (3 x-5)}\]

Answer 6

Step four and five:
Use FOIL, then group like terms.

Answer 7

is that is?

Answer 8

Well no, you could continue to FOIL this:
\[\frac{(7x + 5) (x-1)}{2x(3x-5)}\]
When would in the end give you:
\[\frac{7 x^2-2 x-5}{6 x^2-10 x}\]

Answer 9

What a long a tedious process :-P.
If you wanted to expand that last part you would get:
\[\frac{7 x^2}{6 x^2-10 x}-\frac{2 x}{6 x^2-10 x}-\frac{5}{6 x^2-10 x}\]
Expanding is completely optional!