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4 divided by the sum of x and 2 equals the quotient of 3 and the difference of x and 2.
Solve for x.

Sagot :

danielgeyfman

Answer:

[tex]x=14[/tex]

Step-by-step explanation:

[tex]4[/tex] divided by the sum of [tex]x[/tex] and [tex]2[/tex], in math lingo, is [tex]4/(x+2)[/tex]. The quotient of [tex]3[/tex] and the difference of [tex]x[/tex] and [tex]2[/tex], in math lingo, is [tex]3/(x-2)[/tex].

We have that these two quantities are equal, so [tex]4/(x+2)=3/(x-2)[/tex].

We can multiply both sides of the equation by [tex](x+2)(x-2)[/tex] to get [tex]4(x-2)=3(x+2)[/tex].

We can distribute both sides of the equation to get [tex]4x-8=3x+6[/tex].

We can subtract [tex]3x[/tex] from both sides of the equation to get [tex]x-8=6[/tex].

We can then add [tex]8[/tex] to both sides of the equation to get [tex]x=14[/tex].

So, the answer is [tex]\boxed{x=14}[/tex] and we're done!

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