How did the fifteenth amendment and the 1960s civil rights laws extend voting rights to more americans?

The Fifteenth Amendment was created to prevent people from forbidding others to vote based on their race, color, or previous condition of servitude, which means that it was illegal to forbid African-Americans from voting. The civil right laws removed other racist things that were imposed to still prevent them such as an obligatory literacy test and other things that were created in the south to prevent African-American voters.