What is the answer to ((x^2+3))/((x-3))-((x+6))/((3-x))=1 ?

The answer to ((x^2+3))/((x-3))-((x+6))/((3-x))=1 is x=2sqrt(3)i,x=-2sqrt(3)i

Solve for x: ((x^2+3))/((x-3))-((x+6))/((3-x))=1

The solution is x=2sqrt(3)i,x=-2sqrt(3)i

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\frac{( x ^{2} + 3 )}{( x - 3 )} - \frac{( x + 6 )}{( 3 - x )} = 1

x = 23 i, x = - 23 i

Solution steps

\frac{( x ^{2} + 3 )}{( x - 3 )} - \frac{( x + 6 )}{( 3 - x )} = 1

Multiply by LCM

(x^{2} + 3) (- x + 3) - (x + 6) (x - 3) = (x - 3) (- x + 3)

Solve

(x^{2} + 3) (- x + 3) - (x + 6) (x - 3) = (x - 3) (- x + 3) : x = 3, x = 23 i, x = - 23 i

x = 3, x = 23 i, x = - 23 i

Verify Solutions

Find undefined (singularity) points:

x = 3

Since the equation is undefined for:

3

x = 23 i, x = - 23 i

(x^{4})^{2} = \frac{2 ^{12}}{x ^{5}}

\frac{( x + 1 ) ^{2} + 14}{4 x + 5} = n

\frac{1}{x ^{2}} - \frac{5}{x} + 2 = 0

\frac{5}{( 2 x ^{2} )} - \frac{1}{( 6 x ^{2} )} = \frac{7}{12}

0 = \frac{2}{3 x + 2}

What is the answer to ((x^2+3))/((x-3))-((x+6))/((3-x))=1 ?
The answer to ((x^2+3))/((x-3))-((x+6))/((3-x))=1 is x=2sqrt(3)i,x=-2sqrt(3)i
Solve for x: ((x^2+3))/((x-3))-((x+6))/((3-x))=1
The solution is x=2sqrt(3)i,x=-2sqrt(3)i