(x^(2))/(x-2)+(4)/(2-x) Which of the following is equivalent to the given expression shown for x!=2 ? Choose 1 answer: (A) x+2 (B) x-2 (C) (x^(2)-4)/(2-x) (D) (x^(2)+4)/(x-2)

Rewrite common denominator: We have the expression (x^2)/(x-2) + 4/(2-x). Notice that the denominators (x-2) and (2-x) are opposites of each other. We can rewrite 2-x as -(x-2) to have a common denominator.Combine fractions: Rewrite the second term with the common denominator: 4/(2-x) becomes -4/(x-2).Combine numerators: Now, combine the two fractions with the common denominator: (x^2)/(x-2) - 4/(x-2).Factor numerator: Combine the numerators over the common denominator: (x^2 - 4)/(x-2).Factor difference of squares: Notice that x^2 - 4 is a difference of squares, which can be factored into (x+2)(x-2).Factor numerator: Factor the numerator: (x^2 - 4) becomes (x+2)(x-2).Cancel common factor: Now the expression is ((x+2)(x-2))/(x-2).Simplified expression: Cancel out the common factor (x-2) from the numerator and the denominator.The simplified expression is x+2.

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(x^(2))/(x-2)+(4)/(2-x)
Which of the following is equivalent to the given expression shown for
x!=2 ?
Choose 1 answer:
(A)
x+2
(B)
x-2
(C)
(x^(2)-4)/(2-x)
(D)
(x^(2)+4)/(x-2)

$\frac{x^{2}}{x-2}+\frac{4}{2-x}$ $\newline$ Which of the following is equivalent to the given expression shown for $x \neq 2$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $x+2$ $\newline$ (B) $x-2$ $\newline$ (C) $\frac{x^{2}-4}{2-x}$ $\newline$ (D) $\frac{x^{2}+4}{x-2}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\frac{x^{2}}{x-2}+\frac{4}{2-x}

\newline

Which of the following is equivalent to the given expression shown for

x \neq 2

\newline

Choose

1

answer:

\newline

(A)

x+2

\newline

(B)

x-2

\newline

(C)

\frac{x^{2}-4}{2-x}

\newline

(D)

\frac{x^{2}+4}{x-2}

Rewrite common denominator: We have the expression $(x^2)/(x-2) + 4/(2-x)$ . Notice that the denominators $(x-2)$ and $(2-x)$ are opposites of each other. We can rewrite $2-x$ as $-(x-2)$ to have a common denominator.
Combine fractions: Rewrite the second term with the common denominator: $\frac{4}{2-x}$ becomes $-\frac{4}{x-2}$ .
Combine numerators: Now, combine the two fractions with the common denominator: $(x^2)/(x-2) - 4/(x-2)$ .
Factor numerator: Combine the numerators over the common denominator: $(x^2 - 4)/(x-2)$ .
Factor difference of squares: Notice that $x^2 - 4$ is a difference of squares, which can be factored into $(x+2)(x-2)$ .
Factor numerator: Factor the numerator: $(x^2 - 4)$ becomes $(x+2)(x-2)$ .
Cancel common factor: Now the expression is $\frac{(x+2)(x-2)}{x-2}$ .
Simplified expression: Cancel out the common factor $(x-2)$ from the numerator and the denominator.
Simplified expression: Cancel out the common factor $(x-2)$ from the numerator and the denominator.The simplified expression is $x+2$ .