Simplify the rational expression and then add or subtract. Express answers in simplest form and identify all non-permissible values.
(The non-permissible value is not the issue. It is the simplification)
3x + 15/x^2-25 + 4x^2 -1/ 2x^2 + 9x -5
3(x+5)/(x+5)(x-5) + 4x^2 -1/ (x+5)(2x-1)
LCD: (x-5)(x+5)(2x-1)
6x^2+27x-15/(x+5)(x-5)(2x-1) + 2x^2 - 9x -5
8x^2 + 18x - 20/(x-5)(x+5)
2(4x^2+9x-10)/(x+5)(x-5)
(I know this isn't the right answer. Please help me :( )
one way to find your errors is this. Check each line with the same value of x, lets do it with x=0
3x + 15/x^2-25 + 4x^2 -1/ 2x^2 + 9x -5 VALUE: 15/-25 +1/5= -2/5
3(x+5)/(x+5)(x-5) + 4x^2 -1/ (x+5)(2x-1)
Value: 15/-25 + 1/5: -2/5
6x^2+27x-15/(x+5)(x-5)(2x-1) + 2x^2 - 9x -5
Value: -15/-25 + -5 SO THIS LINE IS WRONG RECHECK IT, and relook at the last term.
8x^2 + 18x - 20/(x-5)(x+5)
2(4x^2+9x-10)/(x+5)(x-5)
Thanks :D
To simplify the given rational expression and add or subtract, follow these steps:
Step 1: Factor the expressions in the numerator and denominator separately.
Numerator:
3(x+5) can be factored as 3 * (x+5)
4x^2 - 1 cannot be factored further.
Denominator:
(x+5)(x-5) cannot be factored further.
2x^2 + 9x - 5 cannot be factored further.
Step 2: Identify the Least Common Denominator (LCD).
The LCD is the product of all distinct prime factors raised to their highest power present in any of the denominators. In this case, the denominators are (x+5)(x-5)(2x-1), so the LCD is (x-5)(x+5)(2x-1).
Step 3: Rewrite the rational expression with a common denominator.
Using the LCD, rewrite the rational expression:
[3(x+5) / (x-5)(x+5)] + (4x^2 - 1) / (x+5)(2x-1)
Step 4: Combine the rational expression.
Combine the numerator by adding or subtracting where necessary:
[3(x+5) + (4x^2 - 1)] / (x-5)(x+5)(2x-1)
Simplifying the numerator:
3(x+5) + (4x^2 - 1) = 3x + 15 + 4x^2 - 1 = 4x^2 + 3x + 14
So the simplified rational expression becomes:
(4x^2 + 3x + 14) / (x-5)(x+5)(2x-1)
Note: This is the simplified form of the rational expression. However, at the end of your question, you present a different rational expression without explaining the steps you took to get there, making it impossible to determine if it is correct or not. If you need further assistance, please provide the steps you followed to arrive at your answer.