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Solve the equation by using the LCD.​​ Check your solution(s).

 Jan 30, 2019
 #1
avatar+102417 
+2

The LCD is x ( x - 4)

 

So we have

 

(x - 3 ) x      +  4x (x - 4)           3x (x - 4)      

______           ________   =    ________     

  x(x - 4)          x(x - 4)               x(x - 4) 

 

Since all the denominators are the same, we can forget them and work with the numerators

 

(x - 3)x  + 4x(x - 4)  = 3x (x - 4)

 

x^2 - 3x + 4x^2 - 16x  = 3x^2 - 12x         simplify

 

5x^2 - 19x = 3x^2  - 12x     rearrange  as

 

2x^2 - 7x = 0

 

x( 2x - 7) = 0       set both factors  to 0  and solve for x

 

x = 0                              2x - 7 = 0

                                      2x  = 7

                                        x = 7/2

 

x = 0    cannot be a solution because it makes an original denominator = 0

 

So....x = 7/2  is the only solution

 

I'll leave the checking for you, GameMaster....

 

 

cool cool cool

 Jan 30, 2019

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