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Question

Solve the equations:
3x4+x22x33x4x2+2x+3=5x4+2x27x+35x42x2+7x3.

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Solution

Using ab=a+bab
Apply this property both sides, we get
3x4+x22x33x4x2+2x+3=5x4+2x27x+35x42x2+7x3
6x42x24x6=10x44x214x+6
When x=0, the equation is satisfied. So, one solution is zero.
Now, when x is not equal to zero, cancel x4 on both sides and cancel factor of 2 in the denominator and numerator
3x22x3=52x27x+3
Now after cross multiplying and simplifying the equation, we get
x211x+24=0
(x8)(x3)=0
So, 3 and 8 are also the solution of equation.
So, x=0,3,8 are the solutions.

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