Expressions
Question 7, P.6.7
HW Score: of 10 points
Part 1012
Points: 0 of 1
Save

Simplity the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression in order for it to be equivalent to the original expression.

Simplity the rational expression.

(Simplify your answer. Use positive exponents only.)

Ask by Hall Cervantes. in the United States

Mar 26,2025

Question

Expressions
Question 7, P.6.7
HW Score: of 10 points
Part 1012
Points: 0 of 1
Save

Simplity the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression in order for it to be equivalent to the original expression.

Simplity the rational expression.

(Simplify your answer. Use positive exponents only.)

Ask by Hall Cervantes. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

We start by factoring the numerator and denominator:

1. Factor the numerator:
$$
3x - 15 = 3(x - 5)
$$

2. Factor the denominator:
$$
x^2 - 10x + 25 = (x - 5)^2
$$

3. Rewrite the expression:
$$
\frac{3x-15}{x^2-10x+25} = \frac{3(x-5)}{(x-5)^2}
$$

4. Cancel the common factor $$(x-5)$$, noting that cancellation is valid only if $$(x-5) \neq 0$$ (i.e., $$x \neq 5$$):
$$
\frac{3(x-5)}{(x-5)^2} = \frac{3}{x-5} \quad \text{for } x \neq 5
$$

Thus, the simplified expression is:
$$
\frac{3}{x-5}
$$
and the number that must be excluded from the domain is $$x = 5$$.
Simplify the rational expression: $$ \frac{3x - 15}{x^2 - 10x + 25} = \frac{3}{x - 5} $$ Exclude $$x = 5$$ from the domain.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions