Solve the equation -4/x - 1 = 7/2 - x + 3/x + 1

x=6.566084 or x=−1.066084

Step-by-step explanation:

Let's solve your equation step-by-step.

−4

x

−1=

7

2

−x+

3

x

+1

−4

x

+−1=

7

2

+−x+

3

x

+1

Multiply all terms by x and cancel:

−4+−1x=

7x

2

+(−x)(x)+3+1x

−x−4=−x2+

9

2

x+3(Simplify both sides of the equation)

−x−4−(−x2+

9

2

x+3)=−x2+

9

2

x+3−(−x2+

9

2

x+3)(Subtract -x^2+9/2x+3 from both sides)

x2+

−11

2

x−7=0

For this equation: a=1, b=-5.5, c=-7

1x2+−5.5x+−7=0

x=

−b±√b2−4ac

2a

(Use quadratic formula with a=1, b=-5.5, c=-7)

x=

−(−5.5)±√(−5.5)2−4(1)(−7)

2(1)

x=

5.5±√58.25

2

x=6.566084380618436,−1.0660843806184368

Check answers. (Plug them in to make sure they work.)

x=6.566084(Works in original equation)

x=−1.066084(Works in original equation)

x=6.566084 or x=−1.066084

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