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X-7/3X+1=X+3/X
We move all terms to the left:
X-7/3X+1-(X+3/X)=0
Domain of the equation: 3X!=0
X!=0/3
X!=0
X∈R
Domain of the equation: X)!=0We add all the numbers together, and all the variables
X!=0/1
X!=0
X∈R
X-7/3X-(+X+3/X)+1=0
We get rid of parentheses
X-7/3X-X-3/X+1=0
We calculate fractions
X-X+(-7X)/3X^2+(-9X)/3X^2+1=0
We add all the numbers together, and all the variables
(-7X)/3X^2+(-9X)/3X^2+1=0
We multiply all the terms by the denominator
(-7X)+(-9X)+1*3X^2=0
Wy multiply elements
3X^2+(-7X)+(-9X)=0
We get rid of parentheses
3X^2-7X-9X=0
We add all the numbers together, and all the variables
3X^2-16X=0
a = 3; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·3·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{256}=16$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*3}=\frac{0}{6} =0 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*3}=\frac{32}{6} =5+1/3 $
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