Question

algebra: concepts and connections - plc
adding and subtracting rational expressions
for which rational expressions is (-5) an excluded value? choose two correct answers.
(\frac{x - 5}{x^2 + 5x}) (\frac{x - 3}{x^2 - 25}) (\frac{x + 5}{x - 5}) (\frac{x^2 - 5}{x^2 + 5}) (\frac{2x + 1}{x^2 + 25})

Explanation:

Step1: Define excluded value rule

An excluded value makes the denominator equal to 0. For each expression, set denominator = 0 and solve for $x$.

Step2: Check $\frac{x-5}{x^2+5x}$

Denominator: $x^2+5x = x(x+5)$. Set to 0:
$x(x+5)=0$ → $x=0$ or $x=-5$. So $x=-5$ is excluded.

Step3: Check $\frac{x-3}{x^2-25}$

Denominator: $x^2-25=(x-5)(x+5)$. Set to 0:
$(x-5)(x+5)=0$ → $x=5$ or $x=-5$. So $x=-5$ is excluded.

Step4: Check $\frac{x+5}{x-5}$

Denominator: $x-5=0$ → $x=5$. $x=-5$ is not excluded.

Step5: Check $\frac{x^2-5}{x^2+5}$

Denominator: $x^2+5=0$ → $x^2=-5$, no real solutions. No excluded real values.

Step6: Check $\frac{2x+1}{x^2+25}$

Denominator: $x^2+25=0$ → $x^2=-25$, no real solutions. No excluded real values.

Answer:

$\frac{x-5}{x^2+5x}$, $\frac{x-3}{x^2-25}$