Question

solve the equation

please

Answer 1

Step-by-step explanation:

Given :-

5/(x-3) - 4/(x+4) = 1/x

To find :-

Find the value of x ?

Solution :-

Given equation is 5/(x-3) - 4/(x+4) = 1/x

=> [5(x+4) - 4(x-3)]/(x-3)(x+4) = 1/x

=> (5x+20-4x+12)/(x-3)(x+4) = 1/x

=> (x+32)/(x-3)(x+4) = 1/x

On applying cross multiplication then

=> x(x+32) = (x-3)(x+4)

=> x²+32x = x(x+4)-3(x+4)

=> x²+32x = x²+4x-3x-12

=> x²+32x = x²+x-12

=> x²+32x-x²-x = -12

=> (x²-x²)+(32x-x) = -12

=> 0+31x = -12

=> 31x = -12

=> x = -12/31

Therefore, x = -12/31

Answer:-

The value of x for the given problem -12/31

Check :-

If x = -12/31 then LHS of the equation is

5/(x-3) - 4/(x+4)

=> 5/[(-12/31)-3] -4/[(-12/31)+4]

=> 5/[(-12-93)/31] -4/[(-12+124)/31]

=> 5/(-105/31) - 4/(112)/31

=> (5×-31)/105 - (4×31)/112

=> (-115/105)-(124/112)

=> (-31/21) - (31/28)

=> (-31)[(1/21)+(1/28)]

=> (-31)(21+28)/(21×28)

=> (-31×49)/(21×28)

=> (-31×7)/(21×4)

=>-31/12

And RHS = 1/x

=> 1/(-12/31)

=> -31/12

=> LHS = RHS is true for x = -31/12

Verified the given relations in the given problem.

Answer 2

$\large{\underline{\underline{ \bf{➥Question:-}}}}$

$\bold{ \small \underline{ \mathbb{\underline{SOLVE : }}}}$

$\underline{ \boxed{ \sf{ ✰ \frac{ 5}{x-3} \: - \: \frac{4}{x+4} \: = \: \frac{1}{x} \: }}}$

$\large{\underline{\underline{ \bf{☂Solution:-}}}}$

• Take LCM of (x - 3) , (x + 4) first
• LCM will be (x - 3)(x + 4)

$\large\longmapsto \frac{5 \: (x + 4 \: ) \: - 4 \:(x - 3 \: )}{(x - 3)(x + 4)} = \frac{1}{x}$

• After solving the brackets :

$\large\longmapsto \frac{5x \: + \: 20 \: - \: 4x \: + \: 12 }{ {x}^{2} \: + 4x \: - 3x \: - 12 } = \: \frac{1}{x}$

$\large\longmapsto \frac{x \: + \: 32}{ {x}^{2} \: + x \: - 12 } \: = \: \frac{1}{x}$

• Doing cross multiplication :

$\small\longmapsto \: {x}^{2} \: + \: 32x \: = \: {x}^{2} + x \: - 12$

$\large\longmapsto 32x \: = \: x \: - \: 12$

$\large\longmapsto 32x - x\: = \: - \: 12$

$\longmapsto 31x \: = \: - \: 12$

$\large\longmapsto x \: = \frac{ - 12}{ \: \: \: \: 31}$

$\underline{ \boxed{ \sf{ ⚝ \: \: x \:  =  \:  \dfrac{-12}{ 31} }}}$

$\huge\underline{\overline{\mid{\bold{\bold{Thanks✅}}\mid}}}$