Question

1/x-3-1/x+5=1/6, x not =3, -5. Find x

Answer 1

Answer:

x=-9 and x=7

Step-by-step explanation:

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Answer 2

${ \huge{ ➙ }} \underline{ \underline{{ \huge{ \mathfrak{ \: R}}} \mathfrak{equired} \: \: \: { \huge{ \mathfrak{ S}}} \mathfrak{olution :-}}}$

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$: \longrightarrow\: { \mathtt{ \: \frac{1}{x - 3} - \frac{1}{x + 5} = \frac{1}{6} }}$

Now, take the L.C.M,

$: \longrightarrow\: { \mathtt{ \: \frac{(x + 5) - (x - 3)}{(x - 3)(x + 5)} = \frac{1}{6} }}$

$: \longrightarrow\: { \mathtt{ \: \frac{ \cancel{x} + 5 - \cancel{ x} + 3}{ {x}^{2} + 5x - 3x - 15 } = \frac{1}{6} }}$

Now, cross multiply it,

$: \longrightarrow\: { \mathtt{ \: 8 \times 6 = {x}^{2} + 5x - 3x - 15 }}$

$: \longrightarrow\: { \mathtt{ \:48 = {x}^{2} + 2x - 15 }}$

$: \longrightarrow\: { \mathtt{ \: - 48 + {x}^{2} + 2x - 15 = 0 }}$

$: \longrightarrow\: { \mathtt{ \: {x}^{2} + 2x - 63 = 0 }}$

$: \longrightarrow\: { \mathtt{ \: {x}^{2} + 9x - 7x - 63 = 0 }}$

$: \longrightarrow\: { \mathtt{ \:x(x + 9) - 7(x + 9) = 0 }}$

$: \longrightarrow\: { \mathtt{ \: (x + 9)(x - 7) = 0}}$

Now,

$: \implies\: { \mathtt{ \: x + 9 = 0}} \\ : \implies\: { \mathtt{ \:x = - 9}} \\ \boxed{ \therefore{ \mathtt{ \: \: \: x = - 9}}}$

And,

$: \implies\: { \mathtt{ \:x - 7 = 0}} \\ : \implies\: { \mathtt{ \:x = 7}} \\ \boxed{\therefore{ \mathtt{ \: \: \: x = 7}}}$

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x = -9 and 7 (ans)..

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