### SAT数学：代数例题 6

2019-08-23 SAT-数学 阅读

# SAT Question 6 Article Rank: Medium 难度： 简单 Topic: Algebra, Algebraic Fractions, Solving Quadratics 话题： 代数，代数分数，解二次方程

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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