Question

Solve for x...

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Answer 1

Step-by-step explanation:

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Answer 2

Given equation:

• $\sf \dfrac x {x+1}+\dfrac {x+1}x=\dfrac {34}{15}$

Solution:

Let's assume x/(x+1) be y, then:

$:\implies \sf y+\dfrac 1 y=\dfrac{34}{15}$

Now taking LCM in LHS

$:\implies \sf \dfrac {y^2+1}y=\dfrac{34}{15}$

Now cross multiplication

$:\implies \sf (y^2+1)15=34y$

$:\implies \sf 15y^2+15=34y$

$:\implies \sf 15y^2-34y+15=0$

Now factorising it using middle term splitting.

$:\implies \sf 15y^2-25y-9y+15=0$

$:\implies \sf 5y(3y-5)-3(3y-5)=0$

$:\implies \sf (3y-5)(5y-3)=0$

$:\implies \boxed{\sf y=\dfrac 5 3\;;\;\dfrac 3 5}$

Now substitute value of y=x/(x+1).

$:\implies \sf \dfrac x {x+1}=\dfrac 3 5\;;\;\dfrac x {x+1}=\dfrac 53$

Cross multiplication for both equations

$:\implies\sf {5x}= 3 {(x+1)}\;;\; {3x} = 5{(x+1)}$

$:\implies \sf 5x= 3x+3\;;\; 3x= 5x+5$

$:\implies \sf 5x-3x=3\;;\; -5= 5x-3x$

$:\implies \sf 2x=3\;;\; -5= 2x$

$:\implies \sf x=\dfrac 3 2\;;\;x= \dfrac {-5} 2$

$:\implies \boxed{\sf x=\dfrac 3 2, \dfrac {-5} 2}$

These are the required values of x.