Question
Solve for $x$ :
$\frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5 x}, x \neq 0,-1,2$
$\frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5 x}, x \neq 0,-1,2$
✓
Answer
Solving for $x$,
$\begin{array}{l}\Rightarrow \frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5 x} \\\Rightarrow \frac{4(x-2)+3(x+1)}{2(x+1)(x-2)}=\frac{23}{5 x} \\\Rightarrow \frac{4 x-8+3 x+3}{2\left(x^2+x-2 x-2\right)}=\frac{23}{5 x} \\\Rightarrow \frac{7 x-5}{2\left(x^2-x-2\right)}=\frac{23}{5 x}\end{array}$
Cross multiplying both sides,
$\begin{array}{l}\Rightarrow 5 x(7 x-5)=46\left(x^2-x-2\right) \\\Rightarrow 35 x^2-25 x=46 x^2-46 x-92\end{array}$
Re-arranging the terms,
$\Rightarrow 11 x^2-21 x-92=0$
Solving the above quadratic equation by splitting the middle term,
$\begin{array}{l}\Rightarrow 11 x^2-44 x+23 x-92=0 \\\Rightarrow 11 x(x-4)+23(x-4)=0 \\\Rightarrow(11 x+23)(x-4)=0\end{array}$
Hence $x=4 \quad$ and $x=-\frac{23}{11}$
$\begin{array}{l}\Rightarrow \frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5 x} \\\Rightarrow \frac{4(x-2)+3(x+1)}{2(x+1)(x-2)}=\frac{23}{5 x} \\\Rightarrow \frac{4 x-8+3 x+3}{2\left(x^2+x-2 x-2\right)}=\frac{23}{5 x} \\\Rightarrow \frac{7 x-5}{2\left(x^2-x-2\right)}=\frac{23}{5 x}\end{array}$
Cross multiplying both sides,
$\begin{array}{l}\Rightarrow 5 x(7 x-5)=46\left(x^2-x-2\right) \\\Rightarrow 35 x^2-25 x=46 x^2-46 x-92\end{array}$
Re-arranging the terms,
$\Rightarrow 11 x^2-21 x-92=0$
Solving the above quadratic equation by splitting the middle term,
$\begin{array}{l}\Rightarrow 11 x^2-44 x+23 x-92=0 \\\Rightarrow 11 x(x-4)+23(x-4)=0 \\\Rightarrow(11 x+23)(x-4)=0\end{array}$
Hence $x=4 \quad$ and $x=-\frac{23}{11}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km upstream and 55km downstream. Determine the speed of stream and that of the boat in still water.
Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis:
x - y + 3 = 0, 2x + 3y - 4 = 0
x - y + 3 = 0, 2x + 3y - 4 = 0
Very-Short-Answer Question:
If (a - b), a and (a + b) are zeros of the polynomial $2x^3 - 6x^2 + 5x - 7$, write the value of a.
→If (a - b), a and (a + b) are zeros of the polynomial $2x^3 - 6x^2 + 5x - 7$, write the value of a.
A train travels at a certain average speed for a distance of 54km and then travels a distance of 63km at an average of 6km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?
Prove that both the roots of the equation (x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0 are real but they are equal only when a = b = c.
If $(m+1)^{\text {th }}$ term of an A.P is twice the $(n+1)^{\text {th }}$ term, prove that $(3 m+1)^{\text {th }}$ term is twice the $(m+n+1)^{\text {th }}$ term.
→Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3).
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
The adjacent sides of a parallelogram ABCD measure 34cm and 20cm, and the diagonal AC measures 42cm. Find the area of the parallelogram.
The area of a right-triangle is 600cm$^2$. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
→