1/x+2 + 1/x = 3/4.
Solve the quadratic equation please
Answers
Answer:
x = 4 \: Or \: x = \frac{-2}{9}x=4Orx=
9
−2
Step-by-step explanation:
\begin{lgathered}We \: have \: a \: \\quadratic\: equation\:\\\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}\end{lgathered}
Wehavea
quadraticequation
x−2
x+3
−
x
1−x
=
4
17
\implies \frac{[x(x+3)-(x-2)(1-x)]}{(x-2)x}=\frac{17}{4}⟹
(x−2)x
[x(x+3)−(x−2)(1−x)]
=
4
17
\implies \frac{(x^{2}+3x-(x-x^{2}-2+2x)}{x^{2}-2x}=\frac{17}{4}⟹
x
2
−2x
(x
2
+3x−(x−x
2
−2+2x)
=
4
17
\implies \frac{x^{2}+3x-3x+x^{2}+2}{x^{2}-2x}=\frac{17}{4}⟹
x
2
−2x
x
2
+3x−3x+x
2
+2
=
4
17
\implies \frac{2x^{2}+2}{x^{2}-2x}=\frac{17}{4}⟹
x
2
−2x
2x
2
+2
=
4
17
\* Do the cross multiplication, we get
\implies 4(2x^{2}+2)=17(x^{2}-2x)⟹4(2x
2
+2)=17(x
2
−2x)
\implies 8x^{2}+8=17x^{2}-34x⟹8x
2
+8=17x
2
−34x
\implies 17x^{2}-34x-8x^{2}-8=0⟹17x
2
−34x−8x
2
−8=0
\implies 9x^{2}-34x-8=0⟹9x
2
−34x−8=0
/* Splitting the middle term, we get
\implies 9x^{2}-36x+2x-8=0⟹9x
2
−36x+2x−8=0
\implies 9x(x-4)+2(x-4)=0⟹9x(x−4)+2(x−4)=0
\implies (x-4)(9x+2)=0⟹(x−4)(9x+2)=0
\implies (x-4)=0\: Or \: 9x+2=0⟹(x−4)=0Or9x+2=0
\implies x = 4 \: Or \: x = \frac{-2}{9}⟹x=4Orx=
9
−2
Therefore,
x = 4 \: Or \: x = \frac{-2}{9}x=4Orx=
9
−2