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How do you simplify #9/(x-4) - 5/x#?

Answer 1

Eva Adamson

#=> color(brown)((4 * (x + 5)) /(x * (x - 4))#

#9 / (x - 4) - 5/x#

#=>( 9x - 5 * (x-4)) / (x * (x-4)), " taking " x * (x-4) " "as " "L C M#

#=> (9x - 5x + 20 ) / (x^2 - 4x), " removing bracket in the numerator"#

#=> (4x + 20) /(x^2 - 4x)#

#=> color(brown)((4 * (x + 5)) /(x * (x - 4))#

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Answer 2

Isaiah Anthony

To simplify the expression 9/(x-4) - 5/x, you need to find a common denominator and combine the fractions. The common denominator is (x-4)x. Multiply the first fraction by x/x and the second fraction by (x-4)/(x-4). This gives you (9x - 36 - 5(x-4))/(x-4)x. Simplify the numerator by distributing and combining like terms: (9x - 36 - 5x + 20)/(x-4)x. Combine like terms further: (4x - 16)/(x-4)x. The expression is now simplified.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.