To simplify the expression, we first find a common denominator for the two fractions. The common denominator would be the product of the two denominators: (x^2-7x+10)(x^2-4).
Next, we use this common denominator to express each fraction with the common denominator:
\frac{3}{x^2-7x+10} - \frac{5x}{x^2-4} = \frac{3(x^2-4)}{(x^2-7x+10)(x^2-4)} - \frac{5x(x^2-7x+10)}{(x^2-7x+10)(x^2-4)}
Simplifying further:
= \frac{3x^2-12}{(x^2-7x+10)(x^2-4)} - \frac{5x^3-35x^2+50x}{(x^2-7x+10)(x^2-4)}
Now, to combine the two fractions, we need a common numerator. We can find a common numerator by multiplying each term by the expansion of the other numerator. However, this would result in a very long expression.
Therefore, we can leave the expression as it is. The restriction would be any value of x for which the denominators (x^2-7x+10) and (x^2-4) are equal to zero. To find these values, we can set each denominator equal to zero and solve for x:
For x^2-7x+10 = 0:
(x-5)(x-2) = 0
x = 5 or x = 2
For x^2-4 = 0:
(x+2)(x-2) = 0
x = -2 or x = 2
Therefore, the restriction is x ≠ -2, 2, 5.
simplify the following polynomial expression and state restriction.
a)\frac{3}{x^2-7x+10}-\frac{5x}{x^2-4}
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