what is the least common denominator of (x-4/5x^2-14x-3)-(2x/10x^2-3x-1)+(7x-2/2x^2-7x+3)
To find the least common denominator (LCD) of the given expression, we need to factor the denominators and identify the shared factors.
Let's factor the denominators individually:
For the first fraction, x - 4 / (5x^2 - 14x - 3), the denominator cannot be factored further as it is a quadratic equation without any common factors.
For the second fraction, 2x / (10x^2 - 3x - 1), the denominator can be factored as (2x - 1)(5x + 1).
For the third fraction, 7x - 2 / (2x^2 - 7x + 3), the denominator can be factored as (2x - 1)(x - 3).
Now we have the factored denominators:
(5x^2 - 14x - 3), (2x - 1)(5x + 1), and (2x - 1)(x - 3).
To find the LCD, we need to identify the highest power of each factor. In this case, the factor (5x + 1) appears in the second fraction, and the factor (x - 3) appears in the third fraction.
Therefore, the LCD of the expression is:
(5x^2 - 14x - 3)(2x - 1)(x - 3).
So, the least common denominator is (5x^2 - 14x - 3)(2x - 1)(x - 3).