rational equation

[Kyle Concannon]

I have tried to complete this problem.

2/x+5 - 3/x+3 = 1/x

note the 2 is above x+5 with a line______ between them. I am assuming its division then minus 3 over x +3 line which = 1 over x.

 

[stapel]

In "inline" formatting, you've got:

. . . . .2/(x + 5) - 3/(x + 3) = 1/x

(Parentheses make a big difference. Parentheses are your friend.)

To solve, multiply through by the common denominator of x(x + 5)(x + 3). (Do not multiply this out; just multiply through.) You should get something along the lines of:

. . . . .\(\displaystyle 2x(x\mbox{ }+\mbox{ }3)\mbox{ }-\mbox{ } 3x(x\mbox{ }+\mbox{ }5)\mbox{ }=\mbox{ }1(x\mbox{ }+\mbox{ }5)(x\mbox{ }+\mbox{ }3)\)

Solve by the usual methods. Remember to check your solution(s) in the original equation, to make sure you're not dividing by zero.

Eliz.

 

[Denis]

2/(x + 5) - 3/(x + 3) = 1/x

Just another way that I like; rearrange:
2/(x + 5) = 1/x + 3/(x + 3)
Now apply lcd x(x + 3) to right side.
Then crisscross multiply...

The shorter the lcd, the better : I'm lazy :shock: