Simplify the following expression completely. (x^(2)+x-90)/(x^(2)+15 x+50) Answer:

Identify expression: Identify the expression to be simplified: (x^2 + x - 90) / (x^2 + 15x + 50).Factor numerator: Factor the numerator x^2 + x - 90. We look for two numbers that multiply to -90 and add to 1. These numbers are 10 and -9. So, x^2 + x - 90 factors to (x + 10)(x - 9).Factor denominator: Factor the denominator x^2 + 15x + 50. We look for two numbers that multiply to 50 and add to 15. These numbers are 10 and 5. So, x^2 + 15x + 50 factors to (x + 10)(x + 5).Write factored form: Write the factored form of the expression: ((x + 10)(x - 9)) / ((x + 10)(x + 5)).Cancel common factors: Cancel out the common factors in the numerator and the denominator. The (x + 10) terms cancel each other out. The simplified form is now (x - 9) / (x + 5).Check further simplification: Check for any further simplification. The expression (x - 9) / (x + 5) cannot be simplified further, as there are no common factors left.

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Q. Simplify the following expression completely.

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\frac{x^{2}+x-90}{x^{2}+15 x+50}

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Answer:

Identify expression: Identify the expression to be simplified: $(x^2 + x - 90) / (x^2 + 15x + 50)$ .
Factor numerator: Factor the numerator $x^2 + x - 90$ . We look for two numbers that multiply to $-90$ and add to $1$ . These numbers are $10$ and $-9$ . So, $x^2 + x - 90$ factors to $(x + 10)(x - 9)$ .
Factor denominator: Factor the denominator $x^2 + 15x + 50$ . We look for two numbers that multiply to $50$ and add to $15$ . These numbers are $10$ and $5$ . So, $x^2 + 15x + 50$ factors to $(x + 10)(x + 5)$ .
Write factored form: Write the factored form of the expression: $\frac{(x + 10)(x - 9)}{(x + 10)(x + 5)}$ .
Cancel common factors: Cancel out the common factors in the numerator and the denominator. The $(x + 10)$ terms cancel each other out. $\newline$ The simplified form is now $(x - 9) / (x + 5)$ .
Check further simplification: Check for any further simplification. The expression $(x - 9) / (x + 5)$ cannot be simplified further, as there are no common factors left.