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Challenge When you simplify algebraic expressions, sometimes the simplified expression is not equivalent to the original for all values of the variable. For example, consider this expression: $$\frac{5 a+10}{a^{2}-4}$$ a. Factor the denominator. For what values of $a$ is the expression undefined? That is, for what values is the denominator equal to 0$?$ b. Now write the expression above using factored forms for both the numerator and denominator. Be sure to look for common factors in the terms. c. Simplify the fraction. d. Now try to evaluate the fraction using each value that made the original expression undefined. You found those values in Part a.) e. You should have seen in Part d the simplified fraction is not equivalent to the original fraction for all values of a. Explain why this happened. f. When you simplify an algebraic fraction, you should note any values of the variable that make the simplified fraction unequal to the original. For example, the fraction $\frac{x(x+1)}{3 x}$ can be simplified as $\frac{x+1}{3},$ where $x \neq 0$ . Simplify the fraction $\frac{2 m+1}{4 m^{2}-1}$

          Challenge When you simplify algebraic expressions, sometimes the simplified expression is not equivalent to the original for all values of the variable. For example, consider this expression:
$$\frac{5 a+10}{a^{2}-4}$$
a. Factor the denominator. For what values of $a$ is the expression undefined? That is, for what values is the denominator equal to 0$?$
b. Now write the expression above using factored forms for both the numerator and denominator. Be sure to look for common factors in the terms.
c. Simplify the fraction.
d. Now try to evaluate the fraction using each value that made the original expression undefined. You found those values in Part a.)
e. You should have seen in Part d the simplified fraction is not equivalent to the original fraction for all values of a. Explain why this happened.
f. When you simplify an algebraic fraction, you should note any values of the variable that make the simplified fraction unequal to the original. For example, the fraction $\frac{x(x+1)}{3 x}$ can be simplified as $\frac{x+1}{3},$ where $x \neq 0$ . Simplify the fraction $\frac{2 m+1}{4 m^{2}-1}$

Added by Victor R.

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