Question

1|x+4-1|=11|30,x≠-4,7​

Answer 1

Step-by-step explanation:

1 Or 2 roots of given Quadratic equation.

Explanation:

Given

\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}

x+4

1

−

x−7

1

=

30

11

\implies \frac{[x-7-(x+4)]}{(x+4)(x-7)}=\frac{11}{30}⟹

(x+4)(x−7)

[x−7−(x+4)]

=

30

11

\implies\frac{x-7-x-4}{x^{2}-7x+4x-28}=\frac{11}{30}⟹

x

2

−7x+4x−28

x−7−x−4

=

30

11

\implies\frac{-11}{x^{2}-3x-28}=\frac{11}{30}⟹

x

2

−3x−28

−11

=

30

11

Do 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

Therefore,

Roots of the given quadratic equation are 1 , 2

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