[tex]\frac{2x-9}{2x-5} -\frac{3x}{2-3x}[/tex]

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вопрос

To simplify the given expression, we need to find a common denominator for the two fractions. The common denominator for [tex]2x-5[/tex] and [tex]2-3x[/tex] is tex(2-3x)[/tex].

So, we rewrite the expression with the common denominator:

[tex]\frac{(2x-9)(2-3x)}{(2x-5)(2-3x)} - \frac{3x(2x-5)}{(2x-5)(2-3x)}[/tex]

Expanding the numerators, we get:

[tex]\frac{4x-6x^2-18+27x}{(2x-5)(2-3x)} - \frac{6x^2-15x}{(2x-5)(2-3x)}[/tex]

Combining like terms:

[tex]\frac{31x-18}{(2x-5)(2-3x)} - \frac{6x^2-15x}{(2x-5)(2-3x)}[/tex]

Now, we combine the fractions:

[tex]\frac{(31x-18) - (6x^2-15x)}{(2x-5)(2-3x)}[/tex]

Simplifying further:

[tex]\frac{31x-18 - 6x^2 + 15x}{(2x-5)(2-3x)}[/tex]

[tex]\frac{-6x^2 + 46x - 18}{(2x-5)(2-3x)}[/tex]

Thus, the simplified expression is [tex]\frac{-6x^2 + 46x - 18}{(2x-5)(2-3x)}[/tex].