Question

please solve this using quadratic equations.
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Step by Step Answer Only!!​

Answer 1

$\frac{x}{x + 1} + \frac{x + 1}{x} = \frac{13}{6}$

Take LCM

$\frac{x(x) + (x + 1)(x + 1)}{x(x + 1)} = \frac{13}{6}$

$\frac{ {x}^{2} + {x}^{2} + 1 + 2x }{ {x}^{2} + x } = \frac{13}{6}$

$\frac{2 {x}^{2} + 2x + 1 }{ {x}^{2} + x} = \frac{13}{6}$

Cross Multiply

$12 {x}^{2} + 12x + 6 = 13 {x}^{2} + 13x$

$6 = 13 {x}^{2} - 12 {x}^{2} + 13x - 12x$

${x}^{2} + x - 6 = 0$

${x}^{2} - 3x + 2x - 6 = 0$

$x(x - 3) + 2(x - 3) = 0$

$(x - 3)(x + 2) = 0$

$x = 3 \: \: or \: \: x = - 2$

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Answer 2

Answer:

x+1

x

+

x

x+1

=

6

13

Take LCM

\frac{x(x) + (x + 1)(x + 1)}{x(x + 1)} = \frac{13}{6}

x(x+1)

x(x)+(x+1)(x+1)

=

6

13

\frac{ {x}^{2} + {x}^{2} + 1 + 2x }{ {x}^{2} + x } = \frac{13}{6}

x

2

+x

x

2

+x

2

+1+2x

=

6

13

\frac{2 {x}^{2} + 2x + 1 }{ {x}^{2} + x} = \frac{13}{6}

x

2

+x

2x

2

+2x+1

=

6

13

Cross Multiply

12 {x}^{2} + 12x + 6 = 13 {x}^{2} + 13x12x

2

+12x+6=13x

2

+13x

6 = 13 {x}^{2} - 12 {x}^{2} + 13x - 12x6=13x

2

−12x

2

+13x−12x

{x}^{2} + x - 6 = 0x

2

+x−6=0

{x}^{2} - 3x + 2x - 6 = 0x

2

−3x+2x−6=0

x(x - 3) + 2(x - 3) = 0x(x−3)+2(x−3)=0

(x - 3)(x + 2) = 0(x−3)(x+2)=0

x = 3 \: \: or \: \: x = - 2x=3orx=−2

hey this is ur answer .