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SAT数学:代数例题 9

2019-09-12 SAT-数学 阅读

SAT Question
Rank: Medium
Topic: Algebra, Algebraic Fractions, Solving Quadratics

Below is a question from a recent SAT exam. It is a non-calculator question that would typically take a student 1-2 minutes to complete.


What are all the values of x that satisfy the equation above?
(A) –3
(B) 0
(C) 1
(D) –3 and –1

To solve this equation, we need to factorise the top of the fraction. We do this with a method known as the difference of two squares. As and 1 are both square numbers the top of the fraction becomes two brackets containing + and – the square roots of and 1

We can now simplify this fraction as x-1 appears on the top and bottom of the fraction.
x+1=-2
We now solve.
x=-3

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