QuestionDecember 15, 2025

Write the polynomial expression in simplest form: (5x-20)/(x^2)-9cdot (x^2+12x+27)/(x^2)+2x-24 (1 point) The simplified form is square (Keep answer in factored form.) What are the restrictions on the variable? square (Type only the numbers and separate your answers with commas, if needed.)

Write the polynomial expression in simplest form: (5x-20)/(x^2)-9cdot (x^2+12x+27)/(x^2)+2x-24 (1 point) The simplified form is square (Keep answer in factored form.) What are the restrictions on the variable? square (Type only the numbers and separate your answers with commas, if needed.)
Write the polynomial expression in simplest form: (5x-20)/(x^2)-9cdot (x^2+12x+27)/(x^2)+2x-24 (1 point)
The simplified form is square  (Keep answer in factored form.)
What are the restrictions on the variable? square  (Type only the numbers and separate your answers with commas, if needed.)

Solution
4.1(275 votes)

Answer

\frac{5(x+9)}{(x-3)(x+6)} ### 3,-3,-6,4 Explanation 1. Factor all numerators and denominators 5x-20 = 5(x-4); x^2-9 = (x-3)(x+3); x^2+12x+27 = (x+3)(x+9); x^2+2x-24 = (x+6)(x-4) 2. Write the expression with factored terms \frac{5(x-4)}{(x-3)(x+3)} \cdot \frac{(x+3)(x+9)}{(x+6)(x-4)} 3. Cancel common factors (x-4) and (x+3) cancel. 4. Write the simplified form Remaining: \frac{5(x+9)}{(x-3)(x+6)} 5. Find restrictions on x Denominator cannot be zero: x-3=0, x+3=0, x+6=0, x-4=0; so x\neq 3,-3,-6,4

Explanation

1. Factor all numerators and denominators<br /> $5x-20 = 5(x-4)$; $x^2-9 = (x-3)(x+3)$; $x^2+12x+27 = (x+3)(x+9)$; $x^2+2x-24 = (x+6)(x-4)$<br />2. Write the expression with factored terms<br /> $\frac{5(x-4)}{(x-3)(x+3)} \cdot \frac{(x+3)(x+9)}{(x+6)(x-4)}$<br />3. Cancel common factors<br /> $(x-4)$ and $(x+3)$ cancel.<br />4. Write the simplified form<br /> Remaining: $\frac{5(x+9)}{(x-3)(x+6)}$<br />5. Find restrictions on $x$<br /> Denominator cannot be zero: $x-3=0$, $x+3=0$, $x+6=0$, $x-4=0$; so $x\neq 3,-3,-6,4$
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