Solve for x:
2
+1
+
3
2(−2)
=
23
5
Answers
Answer:
The value of x is 4 or -2.09
Solution:
Given that solve for "x"
\frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5x}
x+1
2
+
2(x−2)
3
=
5x
23
On cross multiplication we get,
\frac{2 \times 2 \times(x-2)+3 \times(x+1)}{(x+1) \times 2 \times(x-2)}=\frac{23}{5x}
(x+1)×2×(x−2)
2×2×(x−2)+3×(x+1)
=
5x
23
On simplification we get,
\frac{4 \times(x-2)+3 \times(x+1)}{(x+1) \times 2 \times(x-2)}=\frac{23}{5 x}
(x+1)×2×(x−2)
4×(x−2)+3×(x+1)
=
5x
23
\begin{gathered}\begin{array}{c}{\frac{4 x-8+3 x+3}{(x+1) \times 2 \times(x-2)}=\frac{23}{5 x}} \\\\ {\frac{7 x-5}{(x+1) \times 2 \times(x-2)}=\frac{23}{5 x}}\end{array}\end{gathered}
(x+1)×2×(x−2)
4x−8+3x+3
=
5x
23
(x+1)×2×(x−2)
7x−5
=
5x
23
Again on cross multiplication we get,
\begin{gathered}\begin{array}{l}{(7 x-5) \times(5 x)=23 \times 2 \times(x+1) \times(x-2)} \\\\ {35 x^{2}-25 x=46 x\left(x^{2}-1 x-2\right)} \\\\ {35 x^{2}-25 x=46 x^{2}-46 x-92} \\\\ {46 x-25 x=46 x^{2}-35 x^{2}-92} \\\\ {21 x=11 x^{2}-92} \\\\ {11 x^{2}-21 x-92=0}\end{array}\end{gathered}
(7x−5)×(5x)=23×2×(x+1)×(x−2)
35x
2
−25x=46x(x
2
−1x−2)
35x
2
−25x=46x
2
−46x−92
46x−25x=46x
2
−35x
2
−92
21x=11x
2
−92
11x
2
−21x−92=0
Let us use quadratic formula to solve for "x"
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}x=
2a
−b±
b
2
−4ac
Here a = 11 and b = -21 and c = -92