Free Digital SAT Math Rational Expressions and Equations Quiz

Rational Expressions and Equations

Question 1 of 5

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The function \(f\) is defined by \[ f(x)=\frac{2x^2-7x-15}{x^2-25}. \] The table shows some values of \(f(x)\).

\(x\)	\(-2\)	\(0\)	\(1\)	\(3\)
\(f(x)\)	\(-\dfrac{1}{3}\)	\(\dfrac{3}{5}\)	\(\dfrac{5}{6}\)	\(\dfrac{9}{8}\)

Which of the following gives an expression equivalent to \(f(x)\) wherever \(f\) is defined, together with all values of \(x\) that are excluded from the domain of \(f\)?

Select one option.

\(\dfrac{2x+3}{x+5}\); only \(x=-5\) is excluded
\(\dfrac{2x-3}{x+5}\); \(x=5\) and \(x=-5\) are excluded
\(\dfrac{2x+3}{x-5}\); \(x=5\) and \(x=-5\) are excluded
\(\dfrac{2x+3}{x+5}\); \(x=5\) and \(x=-5\) are excluded
\(\dfrac{2x+3}{x+5}\); \(x=-5\) and \(x=-\dfrac{3}{2}\) are excluded

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