Question
Solve the following equation by factorization$\frac{x+2}{x+3}=\frac{2 x-3}{3 x-7}$
✓
Answer
$
\begin{aligned}
& \frac{x+2}{x+3}=\frac{2 x-3}{3 x-7} \\
& (x+2)(3 x-7)=(2 x-3)(x+3) \\
& \Rightarrow 3 x^2-7 x+6 x-14=2 x^2+6 x-3 x-9 \\
& \Rightarrow 3 x^2-x-14=2 x^2+3 x-9 \\
& \Rightarrow 3 x^2-x-14-2 x^2-3 x+9=0 \\
& \Rightarrow x^2-4 x-5=0 \\
& \Rightarrow x^2-5 x+x-5=0 \\
& x(x-5)+1(x-5)=0 \\
& \Rightarrow(x-5)(x+1)=0
\end{aligned}
$
Either $x-5=0$,
then $x=5$
or
$
x+1=0 \text {, }
$
then $x=-1$
Hence $x=5,-1$.
\begin{aligned}
& \frac{x+2}{x+3}=\frac{2 x-3}{3 x-7} \\
& (x+2)(3 x-7)=(2 x-3)(x+3) \\
& \Rightarrow 3 x^2-7 x+6 x-14=2 x^2+6 x-3 x-9 \\
& \Rightarrow 3 x^2-x-14=2 x^2+3 x-9 \\
& \Rightarrow 3 x^2-x-14-2 x^2-3 x+9=0 \\
& \Rightarrow x^2-4 x-5=0 \\
& \Rightarrow x^2-5 x+x-5=0 \\
& x(x-5)+1(x-5)=0 \\
& \Rightarrow(x-5)(x+1)=0
\end{aligned}
$
Either $x-5=0$,
then $x=5$
or
$
x+1=0 \text {, }
$
then $x=-1$
Hence $x=5,-1$.
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 $6^{\text {th }}$ term of an $A.P.$ is $16$ and the $14^{\text {th }}$ term is $32$ . Determine the $36^{\text {th }}$ term.
→In given figure, ABCD is a kite. AB = AD and BC =CD. Prove that the diagona AC is the perpendirular bisector of the diagonal BD.
In a particular tax period, a trader purchased goods worth $Rs.15,00,000$ and paid a VAT of $Rs.1,35,000.$ During the same period, he sold goods worth $Rs.8,00,000$ taxed at $12\%$ and goods worth $Rs.12,00,000$ taxed at $5\%.$ Calculate his tax liability for this.
→David opened a Recurring Deposit Account in a bank and deposited Rs 300 per month for two years. If he received Rs 7,725 at the time of maturity, find the rate of interest per annum.
In the adjoining figure, the crescent is formed by two circles which touch at the point A. $O$ is the centre of bigger circle. If $CB = 9 cm$ and $DE = 5 cm$, find the area of the shaded portion.
→$A$ solid cone of height $8\ cm$ and base radius $6\ cm$ is melted and recast into identical cones eachof height $2\ cm$ and diameter $1\ cm.$ Find the number of cones formed.
→In a single throw of two dice, find the probability of : an odd number as a sum
The sum of a number and its reciprocal is $4.25.$ Find the number.
→Find the equation of the line, whose x-intercept $= −8$ and y-intercept $= -4$
→Find the value of $x$ given that $A^2=B$ Where $A=\left[\begin{array}{ll}2 & 12 \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}4 & x \\ 0 & 1\end{array}\right]$
→