how do you solve this, its about rational expressions ??
4 /X^2 – 4x+1 + 2/ x^2 -1
You will need brackets to establish the correct order of operations.
The way you typed it, the +1 -1 would cancel and you are left with
4 /X^2 – 4x + 2/ x^2
= 4/x^2 - 4x^3/x^2 + 2/x^2
= (6 - 4x^3)/x^2
I have a strong feeling that is not what you meant.
how do you solve this, its about rational expressions ??
4 2
-------- + --------
X^2–4x+1 x^2-1
To simplify the expression (4 / (X^2 – 4x + 1)) + (2 / (x^2 - 1)), you need to find a common denominator and then combine the fractions. Here are the steps:
Step 1: Factor the denominators
The denominator of the first fraction, X^2 – 4x + 1, cannot be factored further since it does not have any factors that multiply to give 1 and add to give -4.
The denominator of the second fraction, x^2 - 1, can be factored as a difference of squares: (x + 1)(x - 1).
Step 2: Find the least common denominator (LCD)
Since the denominators are (X^2 – 4x + 1) and (x^2 - 1), the LCD will be their product: (X^2 – 4x + 1)(x + 1)(x - 1).
Step 3: Rewrite the fractions with the LCD
To rewrite the fractions with the LCD, multiply both the numerator and denominator of each fraction by the necessary factors.
For the first fraction, multiply the numerator and denominator by (x + 1)(x - 1) to get:
4(x + 1)(x - 1) / [(X^2 – 4x + 1)(x + 1)(x - 1)]
For the second fraction, multiply the numerator and denominator by (X^2 – 4x + 1) to get:
2(X^2 – 4x + 1) / [(X^2 – 4x + 1)(x + 1)(x - 1)]
Step 4: Combine the fractions
Now that both fractions have the same denominator, you can combine them by adding their numerators:
4(x + 1)(x - 1) + 2(X^2 – 4x + 1) / [(X^2 – 4x + 1)(x + 1)(x - 1)]
Step 5: Simplify
Expand and simplify the numerator:
4(x^2 - 1) + 2(X^2 – 4x + 1) / [(X^2 – 4x + 1)(x + 1)(x - 1)]
= 4x^2 - 4 + 2X^2 – 8x + 2 / [(X^2 – 4x + 1)(x + 1)(x - 1)]
= (6x^2 - 8x -2) / [(X^2 – 4x + 1)(x + 1)(x - 1)]
So, the simplified form of the expression is:
(6x^2 - 8x - 2) / [(X^2 – 4x + 1)(x + 1)(x - 1)]