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Vedmedyk [2.9K]
3 years ago
12

Can someone please solve for x:

Mathematics
2 answers:
sesenic [268]3 years ago
5 0
To solve this complex fraction equation, we need to get the same denominator on the left, then combine them to one term. Then we can cross-multiply with the other side.
1/2 + 4/2x = x/2x + 4/2x = (x+4)/2x
Now we have (x+4)/2x = (x+4)/10
cross-multiply:
(x+4)×10 = (x+4)×2x
10x+40 = 2x^2+8x
2 {x}^{2}  + 8x - 10x - 40 = 0 \\ 2 {x}^{2}  - 2x - 40 = 0 \\ 2({x}^{2}  - x - 20) = 0 \\ 2(x - 5)(x + 4) = 0
Therefore x = -4 and x = 5
C) is the correct answer
BabaBlast [244]3 years ago
3 0
Make the denominator into 10x:
5x/10x +20/10x=x(x+4)/10x
5x+20=x(x+4)
5x+20=x²+4x
x²-x-20=0
(x-5)(x+4)=0
x=5 or -4
the third choice is correct. 
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