3 years ago

Determine whether the system has no one, or infinitely many solutions.

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

6 0

This has no solution

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ICE Princess25 [194]

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Final answer will be the choice which matches best with expression

$\frac{x^2+4x-1}{x\left(x+2\right)}$ or

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Step-by-step explanation:

Given expression is:

$\frac{\left(x+5\right)}{\left(x+2\right)}-\frac{\left(x+1\right)}{\left(x^2+2x\right)}$

We begin by factoring denominators:

$=\frac{\left(x+5\right)}{\left(x+2\right)}-\frac{\left(x+1\right)}{x\left(x+2\right)}$

Multiply and divide first term by (x) to make denominators equal.

$=\frac{x\left(x+5\right)}{x\left(x+2\right)}-\frac{\left(x+1\right)}{x\left(x+2\right)}$

Since denominators are equal so we can combine numerators.

$=\frac{x\left(x+5\right)-\left(x+1\right)}{x\left(x+2\right)}$

Now simplify

$=\frac{x^2+5x-x-1}{x\left(x+2\right)}$

$=\frac{x^2+4x-1}{x\left(x+2\right)}$

$=\frac{x^2+4x-1}{x^2+2x}$

Hence final answer will be the choice which matches best with expression

$\frac{x^2+4x-1}{x\left(x+2\right)}$ or

$\frac{x^2+4x-1}{x^2+2x}$

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