(x-5) / (x^2-5x) - (x+5) / (x^2 - 25)?

Question

Subtract and simplify. Remember to include any changes in the domain

Answer 1

You first need to find a common denominator. In this case, it would be the multiple of the two rational expressions:

(x^2-25)(x^2-5x).

Multiply both rational expressions by this denominator and combine the fractions:

[(x-5)(x^2-25) - (x+5)(x^2-5x)]/[(x^2-25)(x^2-5x)]

Remember that:

(x^2-25) = (x+5)(x-5) -------> difference of two squares
(x^2-5x) = x(x-5)

Thus, we have the following substitutions:

Numerator:
(x-5)(x-5)(x+5) - x(x+5)(x-5)

Denominator:
x(x-5)(x+5)(x-5)

In the numerator, you can factor out a (x+5)(x-5) term:

[(x+5)(x-5)][(x-5)-x] -----> -5(x+5)(x-5)

With the numerator and denominator, you can cancel out an
(x+5)(x-5) term. Thus the complete simplified expression is:

-5/[x(x-5)] or -5/[x^2-5x]

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Hope this helps

Answer 2

Sometimes reducing each fraction makes the problem a little easier. This is the case here. Factoring the denominator of the left hand part gives (x-5)/x(x-5). This reduces to 1/x. Factoring the right hand side reduces to (x+5)/(x+5)(x-5). This reduces to 1/(x-5). Now the problem is 1/x-1/(x-5). The common denominator is
x(x-5). Now the problem is 1(x-5)/x(x-5)-1x/x(x-5).
This gives -5/x(x-5).

Answer 3

confirm your grouping symbols. Do you intend (3-(5/2))/(3-(3/2))? if so, you may desire to end the subtraction in the numerator (suited) decrease unfastened the denominator (backside), then divide. Convert 3 to a fraction with a denominator subject-loose with 5/2. Use 2/2 = one million. 3 * (2/2) = 6/2. Now carry out the numerator's subtraction: 6/2 - 5/2 = one million/2 Repeat this technique for the denominator: 6/2 - 3/2 = 3/2 you're left with (one million/2)/(3/2). shop in mind that branch is like multiplication via using the reciprocal, for this reason: (one million*2)/(2*3) = 2/6. decrease this to one million/3. desire that's what you necessary!

Answer 4

((x - 5)/(x^2 - 5x)) - ((x + 5)/(x^2 - 25))
((x - 5)/(x(x - 5))) - ((x + 5)/((x - 5)(x + 5)))
(1/x) - (1/(x - 5))
((x - 5) - x)/(x(x - 5))
(x - 5 - x)/(x(x - 5))
-5/(x^2 - 5x)