Question

If ((x²-9)/(x²+3)) = 4/7 , then x is:​

Answer 1

Answer:

Given equation : \dfrac{x^{2}-9}{x+3}=\dfrac{4}{7}

x+3

x

2

−9

=

7

4

\dfrac{x^{2}-3^{2}}{x+3}=\dfrac{4}{7}

x+3

x

2

−3

2

=

7

4

We can factorize x^2 - 3^2 by the identity a^2 - b^2 = ( a + b )( a - b ) where we can assume a as x and b as 3. So, x^2 - 3^2 = ( x + 3 ) ( x - 3 ).

\dfrac{(x+3)(x-3)}{x+3}=\dfrac{4}{7}

x+3

(x+3)(x−3)

=

7

4

( x - 3 ) = \dfrac{4}{7}

7

4

7( x - 3 ) = 4

7x - 21 = 4

7x = 4 + 21

7x = 25

x = 25 / 7

Therefore the value of x satisfying the equation is 25 / 7 .

Step-by-step explanation:

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Answer 2

$\huge\bf{{\color{navy}{a}}{\color{indigo}{n}}{\color{blue}{s}}{\blue{w}}{\color{skyblue}{e}}{\color{lightblue}{r}}}$

$\small{ }$

$\huge\sf{{\underline{\underline{To~solve~:}}}}$

$\sf \frac{ {x}^{2} - 9 }{ {x}^{2} + 3 } = \frac{4}{7} \\ \sf By \: cross \: multiplication, \: we \: get: \\ \sf 7( {x}^{2} - 9) = 4( {x}^{2} + 3) \\ \sf 7 {x}^{2} - 63 = 4 {x}^{2} +12 \\ \sf 7 {x}^{2} - 4 {x}^{2} = 12 + 63 \\ \sf 3 {x}^{2} = 75 \\ \sf {x}^{2} = \frac{75}{3} \\ \sf {x}^{2} = 25 \\ \sf x = \sqrt{25 } \\ \sf x = 5$

$\small{ }$

$\huge\bold{{\color{navy}{Hope}}~{\color{blue}{it}}~{\color{skyblue}{helps..!!}}}$