Answer:
[tex]\frac{x-5}{5x+4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{5x^2-9x+4}{5x^2-x-4}[/tex] × [tex]\frac{x^2-3x-10}{5x^2+6x-8}[/tex]
Factorise numerator/ denominator of both fractions
= [tex]\frac{(5x-4)(x-1)}{(5x+4)(x-1)}[/tex] × [tex]\frac{(x-5)(x+2)}{(5x-4)(x+2)}[/tex]
Cancel common factors on numerator/ denominator of both fractions
= [tex]\frac{5x-4}{5x+4}[/tex] × [tex]\frac{x-5}{5x-4}[/tex]
Cancel the common factor 5x - 4 on numerator/ denominator, leaving
= [tex]\frac{x-5}{5x+4}[/tex]
