Solve the following equation. show all your work x/x-2+x-1/x+1=-1

Mathematics

2 answers:

Andru [333]2 years ago

6 0

Answer:

X=1

Step-by-step explanation:

dmitriy555 [2]2 years ago

3 0

We hates fractions, yess precious, nasty fracitons

multiply both sides by (x-2)(x+1) to clea fractions
x(x+1)+(x-1)(x-2)=(-1)(x-2)(x+1)
distribute
x^2+x+x^2-3x+2=-x^2+x-2
add like terms
2x^2-2x+2=-x^2+x+2
add x^2 to both sdes
3x^2-2x+2=x+2
minus x from both sides
3x^2-3x+2=2
minus 2 both sides
3x^2-3x=0
factor
(3x)(x-1)=0
set to zero

3x=0
x=0

x-1=0
x=1

x=0 or 1

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Find Horizontal and Vertical asymptotes for y=(x^2 -9)/(4x^2 +1)

Gnom [1K]

Answer: Horizontal asymptote is $\dfrac{1}{4}$ and vertical asymptotes are $\pm \dfrac{1}{2i}$

Step-by-step explanation:

Since we have given that

$y=\dfrac{x^2-9}{4x^2+1}$

We need to find the horizontal and vertical asymptotes.

Since vertical asymptotes will occur where the denominator becomes zero.

So, here denominator is $4x^2+1$

Now,

$4x^2+1=0\\\\4x^2=-1\\\\x^2=\dfrac{-1}{4}\\\\x=\pm \dfrac{1}{2i}$

And the horizontal asympototes will occur when the coefficient of higher degree of numerator is divided by coefficient of higher degree of denominator.

$y=\dfrac{1}{4}$