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Simplify the expressions and solve the equations

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2 Answers

4x2 - x - 14  รท  4x2 + x - 14    
     x - 2                  x + 2
 
dividing by a fraction is the same a multiplying by the reciprocal of the fraction.
So we will change this to multiplication, and factor the quadratics
 
(4x + 7)(x - 2) (4x - 7)(x + 2)
        (x - 2)              (x + 2)
 
(4x + 7)(4x - 7) 
 
16x2 - 49

Comments

Sorry, I forgot to use the reciprocal. The answer should be (4x +7) divided by (4x - 7)
Nkeiruka:
 
 
1. I take your "both equal" as follows

1 / (t - 1) - 3 / (t - 3) = 1 / 4.
 
The LCM on the left is (t-1)(t-3).  The equation is
 
[t - 3 - 3(t - 1)] / (t-1)(t-3)  = 1 / 4.  Never divide by zero, so assume that t is not equal to 1 or t is not equal to 3, or both.
 
Now simplify the above expression as
 
 
[t - 3 - 3t +3 ] / (t-1)(t-3) = 1 / 4
 
Cross-multiply and multiply out the factors.
 
- 8t = t2 - 4t + 3
 
You get
 
t2 + 4t + 3 = 0.
 
Factorize.
 
(t +1) ( t + 3) = 0.
 
So the roots are either t = -1 or t = -3.
 
 
Your Number 2 is NOT an equation, it is just an expression, not equated to anything.  Incomplete?
 
 
Dattaprabhakar (Dr. G.)

Comments