Question
Solve the following equation by factorization $\frac{8}{x+3}-\frac{3}{2-x}=2$
✓
Answer
$
\begin{aligned}
& \frac{8}{x+3}-\frac{3}{2-x}=2 \\
& \frac{16-8 x-3 x-9}{(x+3)(2-x)}=2 \\
& \Rightarrow \frac{-11 x+7}{2 x-x^2+6-3 x}=2 \\
& \Rightarrow-11 x+7=4 x-2 x^2+12-6 x \\
& \Rightarrow-11 x+7-4 x+2 x^2-12+6 x=0 \\
& \Rightarrow 2 x^2-9 x-5=0 \\
& \Rightarrow 2 x^2-10 x+x-5=0 \\
& \Rightarrow 2 x(x-5)+1(x-5)=0 \\
& \Rightarrow(x-5)(2 x+1)=0
\end{aligned}
$
Either $x-5=0$,
$
\text { then } x=5
$
or
$
2 x+1=0 \text {, }
$
then $2 x=-1$
$
\Rightarrow x =-\frac{1}{2}
$
Hence $x=5,-\frac{1}{2}$.
\begin{aligned}
& \frac{8}{x+3}-\frac{3}{2-x}=2 \\
& \frac{16-8 x-3 x-9}{(x+3)(2-x)}=2 \\
& \Rightarrow \frac{-11 x+7}{2 x-x^2+6-3 x}=2 \\
& \Rightarrow-11 x+7=4 x-2 x^2+12-6 x \\
& \Rightarrow-11 x+7-4 x+2 x^2-12+6 x=0 \\
& \Rightarrow 2 x^2-9 x-5=0 \\
& \Rightarrow 2 x^2-10 x+x-5=0 \\
& \Rightarrow 2 x(x-5)+1(x-5)=0 \\
& \Rightarrow(x-5)(2 x+1)=0
\end{aligned}
$
Either $x-5=0$,
$
\text { then } x=5
$
or
$
2 x+1=0 \text {, }
$
then $2 x=-1$
$
\Rightarrow x =-\frac{1}{2}
$
Hence $x=5,-\frac{1}{2}$.
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
Find the sum of first $51$ terms of an A.P. whose $2$nd and $3$rd terms are $14$ and $18$ respectively.
→The triangle $A B C$, where $A$ is $(2,6), B$ is $(-3,5)$ and $C$ is $(4,7)$, is reflected in the $y$-axis to triangle $A^{\prime} B^{\prime} C^{\prime}$. Triangle $A^{\prime} B^{\prime} C^{\prime}$ is then reflected in the origin to triangle $A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$.
i. Write down the co-ordinates of $A ^{\prime \prime}, B ^{\prime \prime}$ and $C ^{\prime \prime}$.
ii. Write down a single transformation that maps triangle $A B C$ onto triangle $A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$.
→i. Write down the co-ordinates of $A ^{\prime \prime}, B ^{\prime \prime}$ and $C ^{\prime \prime}$.
ii. Write down a single transformation that maps triangle $A B C$ onto triangle $A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$.
Find $x / y$ when $x^2+6 y^2=5 x y$
→Two circle with centres O and O ' are drawn to intersect each other at points A and B.
Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O ' at A. prove that OA bisects angle BAC.
Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O ' at A. prove that OA bisects angle BAC.
i) In the given figure 3 × CP = PD = 9cm and AP = 4.5 cm Find BP.
Solve $\left(\frac{x}{x+2}\right)^2-7\left(\frac{x}{x+2}\right)+12=0 ; x \neq-2$
→Find the coordinate of a point P which divides the line segment joining :
$M( -4, -5)$ and $N (3, 2)$ in the ratio $2 : 5.$
→$M( -4, -5)$ and $N (3, 2)$ in the ratio $2 : 5.$
In the given figure O is the center of the circle, ∠ BAD = 75° and chord BC = chord CD. Find:
(i) ∠BOC (ii) ∠OBD (iii) ∠BCD.
(i) ∠BOC (ii) ∠OBD (iii) ∠BCD.
The radius of the internal and external surfaces of a hollow spherical shell are $3 cm$ and $5 cm$ respectively! If it is melted and recast into a solid cylinder of height $\frac{8}{3}$ cm, find the diameter of the cylinder.
→A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is $\frac{2}{3}$. Find the number of blue marbles in the jar.
→