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Solve the equation-
[tex] \frac{5}{x - 3} - \frac{4}{x + 4} = \frac{1}{x} [/tex]
​

Sagot :

ᴜᴋɪʏᴏ

Hello studentUnion!

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

Solve the equation-

[tex] \frac{5}{x - 3} - \frac{4}{x + 4} = \frac{1}{x} \\ [/tex]

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

[tex] \frac{5}{x - 3} - \frac{4}{x + 4} = \frac{1}{x} \\ [/tex]

Let's multiply both the sides of the equation by x (x - 3) & (x + 4) which is the LCM of (x - 3), (x + 4) & x. We can't solve it directly without taking the LCM first as the denominators are not equal to each other. Then do cross multiplication. After all these steps, you'll get an equation as..

[tex]x\left(x+4\right)\times 5-x\left(x-3\right)\times 4=\left(x-3\right)\left(x+4\right) \\ [/tex]

Now, use the distributive property & simplify it.

[tex]x\left(x+4\right)\times 5-x\left(x-3\right)\times 4=\left(x-3\right)\left(x+4\right) \\ \left(x^{2}+4x\right)\times 5-x\left(x-3\right)\times 4=\left(x-3\right)\left(x+4\right) \\ 5x^{2}+20x-x\left(x-3\right)\times 4=\left(x-3\right)\left(x+4\right) \\ 5x^{2}+20x-\left(x^{2}-3x\right)\times 4=\left(x-3\right)\left(x+4\right) \\ 5x^{2}+20x-\left(4x^{2}-12x\right)=\left(x-3\right)\left(x+4\right) \\ 5x^{2}+20x-4x^{2}+12x=\left(x-3\right)\left(x+4\right) \\ x^{2}+20x+12x=\left(x-3\right)\left(x+4\right) \\ x^{2}+32x=\left(x-3\right)\left(x+4\right) \\ x^{2}+32x=x^{2}+x-12 \\ x^{2}+32x-x^{2}=x-12 \\ 32x=x-12 \\ 32x-x=-12 \\ 31x=-12 \\ \boxed{ \boxed{ \bf \: x=-\frac{12}{31} }}[/tex]

  • The value of x is -12/31.

__________________

Hope it'll help you!

ℓu¢αzz ッ

Hi1315

Answer:

[tex]\frac{5}{x-3} -\frac{4}{x+4} =\frac{1}{x}[/tex]

[tex]\frac{5(x+4)-4(x-3)}{(x-3)(x+4)} =\frac{1}{x} \\[/tex]

[tex]\frac{5x+20-4x+12}{(x-3)(x+4)} =\frac{1}{x}[/tex]

[tex]\frac{x+32}{(x-3)(x+4)} =\frac{1}{x}[/tex]

Use Cross multiplication

[tex]x(x+32)=(x-3)(x+4)[/tex]

[tex]x^{2} +32x = x^{2} +4x-3x-12[/tex]

[tex]x^{2} +32x=x^{2} +x-12[/tex]

[tex]x^{2} +32x-x^{2} -x=-12[/tex]

[tex]31x = -12[/tex]

[tex]\frac{31x}{31} =\frac{-12}{31} \\x = \frac{-12}{31}[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

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