Question

Simplify:
(2n+3.x (2n+1)(n+2)
(x3)2n+1.x (2n+1)​

Answer 1

Answer:

X=2

Step-by-step explanation:

• a^{b}/a^{c}=a^{b-c}a

b

/a

c

=a

b−c

\quad\quad • (a^{b})^{c}=a^{bc}(a

b

)

c

=a

bc

Now we solve the problem:

\therefore \dfrac{x^{2n+3}.x^{(2n+1)(n+2)}}{(x^{3})^{2n+1}.x^{n(2n+1)}}∴

(x

3

)

2n+1

.x

n(2n+1)

x

2n+3

.x

(2n+1)(n+2)

=\dfrac{x^{2n+3+(2n+1)(n+2)}}{x^{6n+3+n(2n+1)}}=

x

6n+3+n(2n+1)

x

2n+3+(2n+1)(n+2)

=\dfrac{x^{2n+3+2n^{2}+5n+2}}{x^{6n+3+2n^{2}+n}}=

x

6n+3+2n

2

+n

x

2n+3+2n

2

+5n+2

=\dfrac{x^{2n^{2}+7n+5}}{x^{2n^{2}+7n+3}}=

x

2n

2

+7n+3

x

2n

2

+7n+5

=x^{2n^{2}+7n+5-2n^{2}-7n-3}=x

2n

2

+7n+5−2n

2

−7n−3

=x^{2}=x

2

\Rightarrow \dfrac{x^{2n+3}.x^{(2n+1)(n+2)}}{(x^{3})^{2n+1}.x^{n(2n+1)}}=x^{2}⇒

(x

3

)

2n+1

.x

n(2n+1)

x

2n+3

.x

(2n+1)(n+2)

=x2

I. hope it will be helpful to you ☺️