SOLUTION: 4. Solve {{{40/(2x-3)+30/(4x+5)=-11}}}

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Question 143730: 4. Solve 40%2F%282x-3%29%2B30%2F%284x%2B5%29=-11



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
40%2F%282x-3%29%2B30%2F%284x%2B5%29=-11 Start with the given equation


Multiply both sides by the LCD %282x-3%29%284x%2B5%29. This will clear the fractions.



40%284x%2B5%29%2B30%282x-3%29=-11%282x-3%29%284x%2B5%29 Distribute and multiply


160x%2B200%2B60x-90=-11%282x-3%29%284x%2B5%29 Distribute again


160x%2B200%2B60x-90=-11%288x%5E2-2x-15%29 Foil


160x%2B200%2B60x-90=-88x%5E2%2B22x%2B165 Distribute


160x%2B200%2B60x-90%2B88x%5E2-22x-165=0 Add 88x^2 to both sides. Subtract 22x from both sides. Subtract 165 from both sides.


88x%5E2%2B198x-55=0 Combine like terms



11%282x%2B5%29%284x-1%29=0 Factor the left side



Now set each factor equal to zero:

2x%2B5=0 or 4x-1=0

x=-5%2F2 or x=1%2F4 Now solve for x in each case


So our answers are

x=-5%2F2 or x=1%2F4