Question

1/x+4 - 1/x-7 = 11/30 solve this using completing the square method where x is not equal to -4,7​

Answer 1

Step-by-step explanation:

1 1. 11

------ - ------ = --

x+4. x-7. 30

x-7-(x+4) 11

------------- = ---

(x+4)(x-7) 30

x-7-x-4 11

------------------ = --

x(x-7)+4(x-7) 30

-11. 11

------------------- = ---

x^2-7x+4x-28. 30

-1. 1

---------------- = --

x^2-3x-28. 30

x^2-3x-28=-30

x^2-3x-28+30=0

x^2-3x+2=0

Using completing squaring method:

x^2-3x=-2

x^2-x.3=-2

2

x^2- --.x.3=-2

2

x^2-2.x.3/2=-2

x^2-2.x.3/2+(3/2)^2=-2+(3/2)^2

(x+3/2)^2=-2+9/4

(x+3/2)^2=-8+9/4

(x+3/2)^2=1/4

x+3/2=√1/4 ,-√1/4

x+3/2=1/2 ,x+3/2=-1/2

x=1/2-3/2 ,x=-1/2-3/2

x=-2/2 ,x=-4/2

x=-1. ,x=-2

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