Add or subtract rational expressions.
16x-12/4x^2+5x-6-3/x+2
I attempted this question yesterday.
Had some doubts about the typing
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To add or subtract rational expressions, you'll need to find a common denominator. Follow these steps:
Step 1: Simplify each rational expression separately, if possible.
In this case, the first rational expression is (16x - 12) / (4x^2 + 5x - 6), which cannot be simplified further. The second rational expression is 3 / (x + 2), which is already in its simplest form.
Step 2: Find the least common denominator (LCD) between the denominators.
The denominators in this case are (4x^2 + 5x - 6) and (x + 2). To find the LCD, factor each denominator completely. The factors of (4x^2 + 5x - 6) are (4x - 1) and (x + 6). The factors of (x + 2) are just (x + 2). Since (4x - 1) and (x + 6) are not common factors, the LCD is their product: (4x - 1)(x + 6)(x + 2).
Step 3: Convert each rational expression to have the LCD as its denominator.
To convert the first rational expression, multiply the numerator and denominator by (x + 2):
[(16x - 12)(x + 2)] / [(4x^2 + 5x - 6)(x + 2)].
The second rational expression is already in the right form.
Step 4: Perform the addition or subtraction operation.
Now that the rational expressions have the same denominator, you can combine them by adding or subtracting the numerators. In this case, we subtract the second rational expression from the first:
[(16x - 12)(x + 2)] / [(4x^2 + 5x - 6)(x + 2)] - [3(x + 6)] / [(4x - 1)(x + 6)(x + 2)].
Step 5: Simplify the resulting expression, if possible.
Since we have the same denominator, we can combine the numerators:
[(16x - 12)(x + 2) - 3(x + 6)] / [(4x^2 + 5x - 6)(x + 2)].
To simplify further, expand and combine like terms in the numerator:
[16x^2 + 32x - 12x - 24 - 3x - 18] / [(4x^2 + 5x - 6)(x + 2)].
Simplifying the numerator:
[16x^2 + 20x - 42] / [(4x^2 + 5x - 6)(x + 2)].
And that's the final answer.