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Solve each of the following equations.

0 votes

Solve each of the following equations.

asked Oct 15, 2018 in ALGEBRA 2 by anonymous

1 Answer

0 votes

a)

1 / (1 + x)   =   1 - [ 5 / (2x - 4) ]

1 / (1 + x)   =   [ 1(2x - 4) - 5 ] / (2x - 4)

1 / (1 + x)   =   [ 2x - 4 - 5 ] / (2x - 4)

1 / (1 + x)   =   [ 2x - 9 ] / (2x - 4)

Apply Cross Multiplication

1(2x - 4)   =   [ 2x - 9 ](1 + x) 

2x - 4   =   2x(1 + x) - 9(1 + x) 

2x - 4   =   2x + 2x^2 - 9 - 9x 

2x + 2x^2 - 9 - 9x  - (2x - 4)  =  0

2x + 2x^2 - 9 - 9x  - 2x + 4  =  0

2x^2 - 9x - 5  =  0

2x^2 - 10x + x - 5  =  0

2x(x - 5) + 1(x - 5)  =  0

(x - 5)(2x + 1)  =  0

(x - 5)  =  0       ;        (2x + 1)  =  0

x  =  5              ;        2x  =  - 1

x  =  5              ;        x  =  - 1/2

b)

x + 3 + 3/(x - 1)  =  (4 - x) / (x - 1)

[ x(x - 1)+ 3(x - 1)+ 3 ] / (x - 1)  =  (4 - x) / (x - 1)

[ x^2 - x + 3x - 3 + 3 ]  =  (4 - x)

x^2 + 2x ]  =  (4 - x)

x^2 + 2x - 4 + x  =  0

x^2 + 3x - 4  =  0

x^2 + 4x - x - 4  =  0

x(x + 4) - 1(x + 4)  =  0

(x + 4)(x - 1)  =  0

(x + 4)  =  0       ;        (x - 1)  =  0

x  =  - 4             ;         x  =  1

But if we submit x = 1 in the given equation it is undefined

Hence, The solution is x = - 4

Answer : 

a) The solutions are x = 5  and  x = - 1/2

b) The solution is x = - 4.

answered Oct 16, 2018 by homeworkhelp Mentor

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