(3x+4)/(3x-4)+(3x-4)/(3x+4)
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(3x-4)/(3x+4)-(3x+4)/(3x-4)
Very Big Problem and help would be greatly appreciated
not that tough once you notice that your question has the pattern
(a/b + b/a)÷(b/a - a/b)
where a = 3x+4 and b=3x-4
this easily reduces to (a^2 + b^2)/(b^2 - a^2)
now replace a and b with 3x+4 and 3x-4 and it simplifies to
(9x^2+16)/(-24x)
To solve the given expression, we can simplify it by observing the pattern and applying some algebraic manipulations.
First, let's rewrite the expression:
(3x+4)/(3x-4) + (3x-4)/(3x+4)
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(3x-4)/(3x+4) - (3x+4)/(3x-4)
Now, notice that both the numerator and denominator of the fraction have the same format: a/b + b/a and b/a - a/b. In this case, let's let a = 3x+4 and b = 3x-4.
By substituting these values into the equation, we have:
(a/b + b/a) / (b/a - a/b)
Simplifying this expression, we get:
((a^2 + b^2) / (ab)) / ((b^2 - a^2) / (ab))
Next, we can simplify further by canceling out the common factor of ab:
(a^2 + b^2) / (b^2 - a^2)
Now, let's substitute the original values of a and b back into the equation:
( (3x+4)^2 + (3x-4)^2 ) / ( (3x-4)^2 - (3x+4)^2 )
Expanding the square terms, we have:
( 9x^2 + 24x + 16 + 9x^2 - 24x + 16 ) / ( 9x^2 - 16 - 9x^2 - 16 )
Combining like terms, we get:
( 18x^2 + 32 ) / ( -32 )
Finally, we simplify the expression further:
( 9x^2 + 16 ) / ( -16x )
Therefore, the simplified expression is:
(9x^2 + 16) / (-16x)