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( 4 ) \frac { x } { 2 x - 5 } + \frac { 5 } { 5 - 2 x } = 1
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4x-5=2x-5
Variable x cannot be equal to \frac{5}{2} since division by zero is not defined. Multiply both sides of the equation by 2x-5, the least common multiple of 2x-5,5-2x.
4x-5-2x=-5
Subtract 2x from both sides.
2x-5=-5
Combine 4x and -2x to get 2x.
2x=-5+5
Add 5 to both sides.
2x=0
Add -5 and 5 to get 0.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since 2 is not equal to 0, x must be equal to 0.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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