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受欢迎的代数 >

2x^2+1= 1/((x^2)-4)

解答

2 x^{2} + 1 = \frac{1}{( x ^{2} ) - 4}

解答

x = \frac{7 + 89}{2}, x = - \frac{7 + 89}{2}, x = \frac{7 - 89}{4}, x = - \frac{7 - 89}{4}

求解步骤

2 x^{2} + 1 = \frac{1}{( x ^{2} ) - 4}

化简

\frac{1}{( x ^{2} ) - 4} : \frac{1}{x ^{2} - 4}

2 x^{2} + 1 = \frac{1}{x ^{2} - 4}

在两边乘以

x^{2} - 4

2 x^{2} (x^{2} - 4) + x^{2} - 4 = 1

解

2 x^{2} (x^{2} - 4) + x^{2} - 4 = 1 : x = \frac{7 + 89}{2}, x = - \frac{7 + 89}{2}, x = \frac{7 - 89}{4}, x = - \frac{7 - 89}{4}

x = \frac{7 + 89}{2}, x = - \frac{7 + 89}{2}, x = \frac{7 - 89}{4}, x = - \frac{7 - 89}{4}

验证解

找到无定义的点（奇点）:

x = 2, x = - 2

将不在定义域的点与解相综合:

x = \frac{7 + 89}{2}, x = - \frac{7 + 89}{2}, x = \frac{7 - 89}{4}, x = - \frac{7 - 89}{4}

作图

流行的例子

1/(x+1)+3=(13)/(x+1)

\frac{1}{x + 1} + 3 = \frac{13}{x + 1}

1/(x-5)+3=(5x)/(x-5)

\frac{1}{x - 5} + 3 = \frac{5 x}{x - 5}

(11)/(x-1)=(15)/(x+14)

\frac{11}{x - 1} = \frac{15}{x + 14}

\frac{6}{x} = \frac{9}{12}

solvefor z,x= y/z

so l v e f or z, x = \frac{y}{z}