Question Bank / Math / Equivalent Expressions

Equivalent expressions SAT question

Math · Advanced Math · Hard · Answer it here, explanation included.

Which expression is equivalent to $\frac{y + 12}{x - 8} + \frac{y ( x - 8 )}{x ^{2} y - 8 x y}$ ?

ExplanationShow

Choice C is correct. Factoring the denominator in the second term of the given expression gives $\frac{y + 12}{x - 8} + \frac{y ( x - 8 )}{x y ( x - 8 )}$ . This expression can be rewritten with common denominators by multiplying the first term by $\frac{x y}{x y}$ , giving $\frac{x y ( y + 12 )}{x y ( x - 8 )} + \frac{y ( x - 8 )}{x y ( x - 8 )}$ . Adding these two terms yields $\frac{x y ( y + 12 ) + y ( x - 8 )}{x y ( x - 8 )}$ . Using the distributive property to rewrite this expression gives $\frac{x y ^{2} + 12 x y + x y - 8 y}{x ^{2} y - 8 x y}$ . Combining the like terms in the numerator of this expression gives $\frac{x y ^{2} + 13 x y - 8 y}{x ^{2} y - 8 x y}$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Drill this skill on Aceit

Adaptive practice, a daily plan, and score tracking take a free account so we can save your work.

Practice this skill

Equivalent expressions SAT question

More Equivalent expressions questions