To simplify the expression, let's factor out common terms and simplify:
First, let's factor out a y from the numerator and denominator of the first term:
= (x-30)/(x^2-100y^2) - 10/(10x-x^2)
Now we can simplify the second fraction by factoring out a 10:
= (x-30)/(x^2-100y^2) - 10/(10(x-y))
Since x^2 - 100y^2 can be factored as (x+10y)(x-10y), we can rewrite the expression as:
= (x-30)/((x+10y)(x-10y)) - 10/(10(x-y))
To combine the terms, we need to find a common denominator:
= (x-30)/((x+10y)(x-10y)) - (10(x+10y))/((x+10y)(x-10y))
Now we can combine the fractions:
= (x-30-10(x+10y))/((x+10y)(x-10y))
= (x-30-10x-100y)/(x^2-100y^2)
= (-9x-100y-30)/(x^2-100y^2)
Therefore, the simplified expression is (-9x-100y-30)/(x^2-100y^2).
To simplify the expression, let's factor out common terms and simplify:
First, let's factor out a y from the numerator and denominator of the first term:
= (x-30)/(x^2-100y^2) - 10/(10x-x^2)
Now we can simplify the second fraction by factoring out a 10:
= (x-30)/(x^2-100y^2) - 10/(10(x-y))
Since x^2 - 100y^2 can be factored as (x+10y)(x-10y), we can rewrite the expression as:
= (x-30)/((x+10y)(x-10y)) - 10/(10(x-y))
To combine the terms, we need to find a common denominator:
= (x-30)/((x+10y)(x-10y)) - (10(x+10y))/((x+10y)(x-10y))
Now we can combine the fractions:
= (x-30-10(x+10y))/((x+10y)(x-10y))
= (x-30-10x-100y)/(x^2-100y^2)
= (-9x-100y-30)/(x^2-100y^2)
Therefore, the simplified expression is (-9x-100y-30)/(x^2-100y^2).