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Help #52

 May 7, 2018
 #1
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52

 

1/x  + 1  / (x + 2)   =   9/40    get a common denominator on the left

 

[ (x + 2 )  +  x ]  /  [ x (x + 2) ] =    9/40        cross-multiply

 

40 [ x + 2 + x   ] =  9 [ x(x + 2) ]      simplify

 

40  [ 2x + 2]   =  9 (x^2 + 2x )

 

80x + 80  = 9x^2  + 18x

 

9x^2  + 18x   =  80x  + 80        subtract  80x, 80  from  both sides

 

9x^2  - 62x  - 80  = 0       factor

 

(9x + 10) (x - 8)  = 0     set each factor to 0  and solve for x

 

9x  + 10  = 0            x - 8  = 0

9x  = -10                   x  = 8

x  = -10/9

 

Since we must have interger answers.....x  = 8    and  x + 2  =  8 + 2  = 10

 

 

cool cool cool

 May 7, 2018

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