Question

plz answer for this question ​

Answer 1

✓ Solution

$\dfrac{ {x}^{2} + 8 }{ {x}^{2} - 4 } \div \dfrac{ {x}^{2} - 2x + 4 }{x + 2}$

Firstly let us simplify all the terms and try to cancel out the common terms.

$\longrightarrow \: {x}^{3} + 8 = {x}^{3} + {2}^{3}$

${a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$

$here \: a = x \: and \: b = 2 \:$

$\bf\implies{x}^{3}+{2}^{3}=(x+2)(x^{2}- 2x+4)$

$\longrightarrow \: {x}^{2} - 4 = {x}^{2} - {2}^{2}$

${a}^{2} - {b}^{2} = (a + b)(a - b)$

$here \: a = x \: and \: b = 2$

$\bf \: \implies \: {x}^{2} - {2}^{2} = (x + 2)(x - 2)$

Now Let's solve it ,

$\dfrac{ {x}^{2} + 8 }{ {x}^{2} - 4 } \div \dfrac{ {x}^{2} - 2x + 4 }{x + 2}$

When we want to convert division into multiplication , we need to reciprocate the other fraction !!

$\dfrac{ {x}^{2} + 8 }{ {x}^{2} - 4 } \times \dfrac{x + 2}{ {x}^{2} - 2x + 4 }$

By substitute the simplified terms , we get

$\dfrac{(x + 2)( {x}^{2} - 2x + 4 )}{(x + 2)( x - 2)} \times \dfrac{x + 2}{ {x}^{2} - 2x + 4 }$

$\bf \: \implies \: \dfrac{x + 2}{x - 2}$

_______________________ .

➻ What's called reciprocal ??

Reciprocal mean we need to change the places of numerator as denominator and vice versa.

➻ Simplifying the terms and solving the terms will make us easy and better.

Answer 2

Answer:

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EXPRESSION —

$\huge \frac{ {x}^{3} + 8 }{ {x}^{2} - 4 } \div \frac{ {x}^{2} - 2x + 4}{x + 2}$

• Firstly we will simplify all the terms and will try to cancel out the common terms

${x}^{3} + 8 = {x}^{3} + {2}^{3}$

We know

$\large\longrightarrow {a}^{3} + {b}^{3 } = (a + b)( {a}^{2} - 2ab + {b}^{2} )$

$here \: a = x \: and \: b = 2$

$\large = ) {x}^{3} + {2}^{3} = (x + 2)( {x}^{2} - 2x - 4)$

${x}^{2} - 4 = {x}^{2} - {2}^{2}$

We Know

$\large\longrightarrow {a}^{2} - {b}^{2} = (a + b)(a - b)$

$here \: a = x \: and \: b = 2$

$\large = ) {x}^{2} - {2}^{2} = (x + 2)(x - 2)$

$\large\boxed{\fcolorbox{red} {black}{\color{yellow}{Solution}}}$

$\huge \frac{ {x}^{3} + 8 }{ {x}^{2} - 4 } \div \frac{ {x}^{2} - 2x + 4}{x + 2}$

• Now we will convert division to multiplication
• When we want to convert them we reciprocate the fraction

$\huge \frac{ {x}^{3} + 8 }{ {x}^{2} - 4 } \times \frac{ (x + 2)}{ {x}^{2} - 2x + 4}$

• Now we will substitute the simplified terms .

$\large \frac{(x + 2)( {x}^{2} - 2x - + 4)}{(x + 2)(x - 2)} \times \frac{(x + 2)}{ {x}^{2} - 2x + 4 }$

$\huge\orange{\boxed{ \longrightarrow \frac{ (x + 2)}{(x - 2)}}}$

$<marquee behaviour-move> <font color="fushsia"> <h1>_____________________</ ht> </marquee>$

Please Note :

Reciprocal means to change the places of numerator and denominator.

Simplifying the terms help us to solve easily .

$<marquee behaviour-move> <font color="fushsia"> <h1>_____________________</ ht> </marquee>$

$\huge{\mathbb{\purple{ Hop{\pink{eIt{\green{H\blue{e{\red{ l{\orange{ps}}}}}}}}}}}}$

$\blue{Mark \: as \: BRAINLIEST \star}</h2><h2></h2><h2>$

$\huge\purple{\mathfrak{@phenom}}$