find the roots of 1/x+4-1/x-7=11/30
Answers
Answered by
6
Step-by-step explanation:
1/x+4 - 1/x-7 = 11/30
x-7-x-4/(x+4)(x-7) = 11/30
-11/(x+4)(x-7) = 11/30
(x+4)(x-7) = -30
x^2-3x-28 = -30
x^2-3x = -2
x^2-3x+2 = 0
x^2-2x-x+2 = 0
x(x-2)-1(x-2) = 0
(x-1)(x-2) = 0
x=1 or 2
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Answered by
9
Answer:
x = 1 , 2
Step-by-step explanation:
Given
1/(x + 4) - 1/(x - 7) = 11/30
=> [x - 7 - (x + 4)] / (x +4)(x - 7) = 11/30
=> (x - 7 - x - 4) / (x^2 - 7x + 4x - 28) = 11/30
=> (- 11) / (x^2 - 3x - 28) = 11/30
By doing the cross multiplication, we get,
=> 30 = 11(x²-3x-28)/(-11)
=> 30 = -(x²-3x-28)
=> x²-3x-28+30 =0
=> x²-3x+2=0
Splitting the middle term, we get
=> x²-1x-2x+2 =0
=> x(x-1)-2(x-1)=0
=> (x-1)(x-2)=0
=>x-1 = 0 or x-2 = 0
=> x = 1 or x = 2
=> x = 1,2
Therefore,
Roots of the given quadratic equation are 1 , 2
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