Multiplying or dividing rational expressions
6x^2 + 13x - 5 divide by 6x^2 -23x + 7
Need to show my work.
On here, we write rational expressions this way:
(6x^2 + 13x - 5)/(6x^2 -23x + 7)
= (3x-1)(2x + 5)/((3x-1)(2x - 7)
= (2x+5)/(2x-7) , x ≠ 1/3 (or else I divided by zero)
To divide rational expressions, you will need to perform polynomial long division. Here are the steps to divide the given rational expressions:
Step 1: Write down the division problem in the long division format, with the dividend (numerator) as the long division inside the bracket, and the divisor (denominator) outside the bracket.
```
6x^2 + 13x - 5
_____________________
6x^2 - 23x + 7 |
```
Step 2: Divide the first term of the dividend (6x^2) by the first term of the divisor (6x^2). Write the result above the line.
```
6x^2 + 13x - 5
_____________________
6x^2 - 23x + 7 | 1
```
Step 3: Multiply the divisor (6x^2 - 23x + 7) by the result obtained in Step 2 (1), and write the product below the dividend. Then subtract the result from the dividend.
```
6x^2 + 13x - 5
_____________________
6x^2 - 23x + 7 | 1
- (6x^2 - 23x + 7)
___________________
36x - 12
```
Step 4: Bring down the next term from the dividend (-5) and continue the process.
```
6x^2 + 13x - 5
_____________________
6x^2 - 23x + 7 | 1
- (6x^2 - 23x + 7)
___________________
36x - 12
- (36x - 12)
_______________
0
```
Step 5: Since there are no more terms left to bring down and divide, and the remainder is zero, the division is complete. The quotient of the division is the result obtained in Step 2 (1).
Therefore, the division of the rational expressions is:
```
6x^2 + 13x - 5
_____________________
6x^2 - 23x + 7 = 1
```
So, the answer is 1.