Mathematics: Solve for x 4/x + 4/x^2-9= 3/x-3 x = –4 and x = –9 x = 4 and x = –9 x = –4 and x = 9 x = 4 and x = 9

Solve for x 4/x + 4/x^2-9= 3/x-3 x = –4 and x - id44293349343502, ashleyrover11

Ответ:

smilebehappy468

10.03.2022

$\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}\qquad\text{subtract}\ \dfrac{4}{x^2-9}\ \text{from both sides}\\\\\dfrac{4}{x}=\dfrac{3}{x-3}-\dfrac{4}{x^2-9}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{4}{x}=\dfrac{3}{x-3}-\dfrac{4}{x^2-3^2}\\\\\dfrac{4}{x}=\dfrac{3}{x-3}-\dfrac{4}{(x-3)(x+3)}\\\\\dfrac{4}{x}=\dfrac{3(x+3)}{(x-3)(x+3)}-\dfrac{4}{(x-3)(x+3)}\qquad\text{use distributive property}\\\\\dfrac{4}{x}=\dfrac{3x+9-4}{(x-3)(x+3)}\\\\\dfrac{4}{x}=\dfrac{3x+5}{x^2-9}\qquad\text{cross multiply}$

$4(x^2-9)=x(3x+5)\qquad\text{use distributive property}\\\\4x^2-36=3x^2+5x\qquad\text{subtract}\ 3x^2\ \text{and}\ 5x\ \text{from both sides}\\\\x^2-5x-36=0\\\\x^2-9x+4x-36=0\\\\x(x-9)+4(x-9)=0\\\\(x-9)(x+4)=0\iff x-9=0\ \vee\ x+4=0\\\\\boxed{x=9\ \vee\ x=-4}$

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Ответ:

rosie81

15.07.2021

Mathematics

The answer in the procedure

Step-by-step explanation:

we know that

If the dilation produces a smaller figure

then

the scale factor must be less than one

Let

z > the scale factor

z < 1

A possible scale factor can be 0.50, 0.20,0.35,0.80, etc

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Solve for x 4/x + 4/x^2-9= 3/x-3 x = –4 and x = –9 x = 4 and x = –9 x = –4 and x = 9 x = 4 and x = 9

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