Rewrite as equivalent rational expressions with denominator (3x-8)(x-5)(x-3)

Question

asked May 21, 2023 92.3k views

1 Answer

Caram · Answer 1 · 2023-05-26T01:30:03+0000

we have the expression

Rewrite as equivalent rational expressions with denominator (3x-8)(x-5)(x-3)

In this problem

3x^2-23x+40=3(x-5)(3x-8)

so

$(4)/(3x^2-23x+40)=(4)/(3\mleft(x-5\mright)\mleft(3x-8\mright))$

Multiply by (x-3)/(x-3)

$(4)/(3(x-5)(3x-8))\cdot((x-3))/((x-3))=(4(x-3))/(3(x-5)(3x-8)(x-3))$

Part 2

we have the expression

we have that

3x^2-17x+24=3(3x-8)(x-3)

so

$(9x)/(3x^2-17x+24)=(9x)/(3\mleft(3x-8\mright)\mleft(x-3\mright))=(3x)/((3x-8)(x-3))$

Multiply the expression by (x-5)/(x-5)

$(3x)/((3x-8)(x-3))\cdot((x-5))/((x-5))=(3x(x-5))/((3x-8)(x-3)(x-5))$