SOLUTION: Please help me with this equation: It is a rational expression and the directions are: Perform the operation and simplify completely: (2x-1) divided by (x+3) minus (1-x) divi

Algebra ->  Rational-functions -> SOLUTION: Please help me with this equation: It is a rational expression and the directions are: Perform the operation and simplify completely: (2x-1) divided by (x+3) minus (1-x) divi      Log On


   

Question 93084This question is from textbook
: Please help me with this equation:
It is a rational expression and the directions are: Perform the operation and simplify completely:
(2x-1) divided by (x+3) minus (1-x) divided by (x+3) This question is from textbook

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
%282x-1%29%2F%28x%2B3%29+-+%281-x%29%2F%28x%2B3%29
.
To perform the operations and simplify completely you first notice that both fractions have
the denominator %28x%2B3%29 in common. Therefore their numerators can be written over the
single common denominator to get:
.
%28%282x-1%29-%281-x%29%29%2F%28x%2B3%29
.
In the numerator the first quantity in parentheses is (2x-1). Since its set of parentheses
is not preceded by a minus sign, you can just remove those parentheses without doing
anything to the terms inside. When you do the problem becomes:
.
%282x-1-%281-x%29%29%2F%28x%2B3%29
.
Notice now the next set of parentheses in the numerator. The terms inside this set of
parentheses are +1 and -x. Since the parentheses are preceded by a minus sign, when you
remove the parentheses you change the sign of all the terms inside. When you do that the
problem then becomes:
.
%282x-1-1%2Bx%29%2F%28x%2B3%29
.
Then you can combine the like terms in the numerator. The +2x and the +x combine to
give +3x and the -1 and -1 combine to give -2. This makes the problem:
.
%283x+-+2%29%2F%28x%2B3%29
.
That's the answer to the problem. There are no other cancellations or combinations
that can be made. If you like you can long divide x + 3 into 3x - 2 and the answer you
will get is:
.
3+-11%2F%28x%2B3%29
.
But that is the same as the answer:
.
%283x+-+2%29%2F%28x%2B3%29
.
It's just in a different form.
.
Hope this helps you to understand what the problem is asking for you to do, and provides
you with some insight into how to do the problem too.