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受欢迎的代数 >

1/((x^2-2x-8))= a/((x-4))+b/((x+2))

解答

\frac{1}{( x ^{2} - 2 x - 8 )} = \frac{a}{( x - 4 )} + \frac{b}{( x + 2 )}

解答

x = \frac{1 - 2 a + 4 b}{a + b}; a \neq = - b

求解步骤

\frac{1}{( x ^{2} - 2 x - 8 )} = \frac{a}{( x - 4 )} + \frac{b}{( x + 2 )}

乘以最小公倍数

1 = a (x + 2) + b (x - 4)

交换两边

a (x + 2) + b (x - 4) = 1

乘开

a (x + 2) : a x + 2 a

a x + 2 a + b (x - 4) = 1

乘开

b (x - 4) : b x - 4 b

a x + 2 a + b x - 4 b = 1

将

2 a

到右边

a x + b x - 4 b = 1 - 2 a

将

4 b

到右边

a x + b x = 1 - 2 a + 4 b

分解

a x + b x : x (a + b)

x (a + b) = 1 - 2 a + 4 b

两边除以

a + b; a \neq = - b

x = \frac{1 - 2 a + 4 b}{a + b}; a \neq = - b

作图

流行的例子

\frac{1}{x ^{2}} = 0

((y^2)/(2y))+3y-5=2

(\frac{y ^{2}}{2 y}) + 3 y - 5 = 2

(x^2+1)/(x^2+1)=0

\frac{x ^{2} + 1}{x ^{2} + 1} = 0

1/5 = x/(x+100)

\frac{1}{5} = \frac{x}{x + 100}

(-2)/(3(2x-4))=3-2(x-8)

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